Filed pursuant to 497(k)

File Nos. 002-84012 and 811-03752

AMG FUNDS III

AMG Managers Special Equity Fund

Supplement dated March 19, 2021 to the Summary Prospectus, dated March 15, 2021

The following information supplements and supersedes any information to the contrary relating to AMG Managers Special Equity Fund (the “Fund”), a series of AMG Funds III (the “Trust”), contained in the Fund’s Summary Prospectus (the “Summary Prospectus”), dated as noted above.

At a meeting held on March 17-18, 2021 (the “Meeting”), the Trust’s Board of Trustees (the “Board”) approved the appointment of Veritas Asset Management LLP (“Veritas” or the “Subadviser”) as the subadviser to the Fund on an interim basis to replace Federated MDTA LLC, Lord, Abbett & Co. LLC, Ranger Investment Management L.P. and Smith Asset Management Group, L.P. (each, a “Former Subadviser” and together, the “Former Subadvisers”), effective March 19, 2021 (the “Implementation Date”). The appointment of Veritas was pursuant to an interim subadvisory agreement between AMG Funds LLC (“AMGF”) and Veritas (the “Interim Subadvisory Agreement”), to be effective until the earlier of 150 days after the termination of the former subadvisory agreement between AMGF and each Former Subadviser with respect to the Fund (each, a “Former Subadvisory Agreement” and together, the “Former Subadvisory Agreements”), which occurred on March 19, 2021, or the approval of a new subadvisory agreement between AMGF and Veritas by the Board and Fund shareholders. At the Meeting, the Board also approved the longer-term appointment of Veritas as the subadviser to the Fund, a new subadvisory agreement between AMGF and Veritas (the “New Subadvisory Agreement”), and the submission of the New Subadvisory Agreement to Fund shareholders for approval. The rate of compensation to be received by Veritas under the Interim Subadvisory Agreement approved by the Board is the same rate of compensation that each Former Subadviser would have received under the applicable Former Subadvisory Agreement.

In connection with the hiring of Veritas, effective as of the Implementation Date, the Fund (i) changed its name from AMG Managers Special Equity Fund to AMG Veritas Asia Pacific Fund, (ii) made changes to its investment objective, principal investment strategies and principal risks, and (iii) replaced its existing benchmark index with the MSCI AC Asia Pacific ex Japan Index.

Also in connection with the hiring of Veritas, the Board approved the following fee changes for the Fund, all of which will be implemented upon the effectiveness of the New Subadvisory Agreement and will result in the overall reduction of the Fund’s net expense ratios: (i) the management fee for the Fund will be reduced from 0.90% to 0.71%; and (ii) the Fund’s existing contractual expense limitation agreement with AMGF will be replaced with a new contractual expense limitation agreement with AMGF pursuant to which AMGF will agree, through at least May 1, 2023, to limit total annual operating expenses (exclusive of taxes, interest (including interest incurred in connection with bank and custody overdrafts and in connection with securities sold short), shareholder servicing fees, distribution and service (12b-1) fees, brokerage commissions and other transaction costs, dividends payable with respect to securities sold short, acquired fund fees and expenses, and extraordinary expenses) of the Fund to the annual rate of 0.93% of the Fund’s average daily net assets, subject to later reimbursement by the Fund in certain circumstances. AMGF pays a portion of the management fee to the Fund’s subadviser for its services.

The disposition of Fund securities in connection with the transition of the Fund’s investment objective and strategies is expected to cause the Fund to realize taxable income for U.S. federal income tax purposes. The Fund intends to make a special distribution to shareholders of all or a portion of such income. This distribution will be taxable to shareholders who hold their shares in a taxable account. See “Certain Federal Income Tax Information” for further information.

In addition, effective as of the Implementation Date, the Summary Prospectus is amended as follows:

All references to the name of the Fund shall refer to AMG Veritas Asia Pacific Fund.

The section titled “Investment Objective” on page 1 is deleted and replaced with the following:

INVESTMENT OBJECTIVE

AMG Veritas Asia Pacific Fund (the “Fund”) seeks to provide long-term capital appreciation.

The section titled “Principal Investment Strategies” beginning on page 1 is deleted and replaced with the following:

PRINCIPAL INVESTMENT STRATEGIES

The Fund principally invests in equity securities listed or traded on exchanges in the Asia Pacific region (excluding Japan). Under normal circumstances, the Fund invests at least 80% of its net assets, plus the amount of any borrowings for investment purposes, in securities of issuers located in the Asia Pacific region (excluding Japan). Under normal circumstances, the Fund considers equity securities to include common and preferred stocks, depositary receipts, and securities with equity characteristics, including, but not limited to, equity-linked notes and participation notes. The Fund considers an issuer to be located in the Asia Pacific region (excluding Japan) if the issuer has its registered office in the Asia Pacific region or has the predominant part of its commercial activity in the Asia Pacific region or, in the case of a holding company, it predominantly holds participations in companies with registered offices in the Asia Pacific region.

The Fund intends to invest in focused equity positions, identified through the bottom-up, stock picking approach of Veritas Asset Management LLP, the subadviser to the Fund (“Veritas” or the “Subadviser”), with a macro overlay. The Subadviser’s macro analysis will focus on identifying long term themes and trends and then proceed to identifying companies within those identified themes and trends that it believes have sound business models, strong management and disciplined financial controls. The Fund seeks to focus on quality companies in sectors that the Subadviser believes show long term structural growth potential with emphasis on industry leaders or emerging leaders with durable competitiveness. The macro themes are identified via a combination of in-house and external research. Asian domestic demand is an example of a theme internal to the Subadviser. In part, the Fund uses this analysis to seek to identify opportunities to invest in companies in the Asia Pacific region whose businesses are benefitting from rising consumer spending in the Asia Pacific region in consumer goods or services.

The Fund intends to gain exposure to equities issued by companies located in the People’s Republic of China (“PRC”) through direct exposure in the Shanghai and Shenzen stock exchanges or indirect exposure through P-Notes or similar equity linked securities. The Fund intends to gain exposure to equities issued by companies located in India through direct exposure or indirect exposure through P-Notes or similar equity linked securities.

The Fund will generally invest in mid- to large-capitalization companies, although the Fund may also invest in small-capitalization companies. The Fund generally invests in companies with market capitalizations greater than $5 billion. The Fund currently expects to hold between 15 and 60 positions at any time.

The Fund may hold assets in cash and cash equivalents, and at times these holdings may be significant. The Fund’s cash level at any point typically relates to the Subadviser’s individual security selection process, and therefore may vary, depending on the Subadviser’s desired security weightings.

The section titled “Principal Risks” beginning on page 2 is revised to remove “Growth Stock Risk,” “Model and Data Risk,” and “Sector Risk” as principal risks of the Fund and to add the following as principal risks of the Fund:

Currency Risk—fluctuations in exchange rates may affect the total loss or gain on a non-U.S. dollar investment when converted back to U.S. dollars and exposure to non-U.S. currencies may subject the Fund to the risk that those currencies will decline in value relative to the U.S. dollar.

Emerging Markets Risk—investments in emerging markets are subject to the general risks of foreign investments, as well as additional risks which can result in greater price volatility. Such additional risks include the risk that markets in emerging market countries are typically less developed and less liquid than markets in developed countries and such markets are subjected to increased economic, political, or regulatory uncertainties.

Focused Investment Risk—to the extent the Fund invests a substantial portion of its assets in a relatively small number of securities or a particular market, industry, group of industries, country, region, group of countries, asset class or sector, it generally will be subject to greater risk than a fund that invests in a more diverse investment portfolio. In addition, the value of the Fund would be more susceptible to any single economic, market, political or regulatory occurrence affecting, for example, that particular market, industry, region or sector.

Geographic Focus Risk—to the extent the Fund focuses its investments in a particular country, group of countries or geographic region, the Fund is particularly susceptible to economic, political, regulatory or other events or conditions affecting such countries or region, and the Fund’s NAV may be more volatile than the NAV of a more geographically diversified fund and may result in losses.

Greater China. The Fund is particularly susceptible to risks in the Greater China region, which consists of Hong Kong, The People’s Republic of China and Taiwan, among other countries. Economies in the Greater China region are dependent on the economies of other countries and can be significantly affected by currency fluctuations and increasing competition from other emerging economies in Asia with lower costs. Adverse events in any one country within the region may impact the other countries in the region or Asia as a whole. Markets in the Greater China region can experience significant volatility due to social, economic, regulatory and political uncertainties. Significant portions of the Chinese securities markets may become rapidly illiquid, as Chinese issuers have the ability to suspend the trading of their equity securities, and have shown a willingness to exercise that option in response to market volatility and other events. U.S. or foreign government restrictions or intervention could negatively affect the implementation of the Fund’s investment strategies, for example by precluding the Fund from making certain investments or causing the Fund to sell investments at disadvantageous times. China has yet to develop comprehensive securities, corporate, or commercial laws, its market is relatively new and less developed, and its economy may be adversely impacted by a slowdown in export growth.

India. In India, the government has exercised and continues to exercise significant influence over many aspects of the economy. Government actions, bureaucratic obstacles and inconsistent economic reform within the Indian government have had a significant effect on its economy and could adversely affect market conditions, economic growth and the profitability of private enterprises in India. Global factors and foreign actions may inhibit the flow of foreign capital on which India is dependent to sustain its growth. Large portions of many Indian companies remain in the hands of their founders (including members of their families). Corporate governance standards of family-controlled companies may be weaker and less transparent, which increases the potential for loss and unequal treatment of investors. India experiences many of the risks associated with developing economies, including relatively low levels of liquidity, which may result in extreme volatility in the prices of Indian securities. Religious, cultural and military disputes persist in India, and between India and Pakistan (as well as sectarian groups within each country).

High Cash Balance Risk—when the Fund has a significant cash balance for a sustained period, the benefit to the Fund of any market upswing may likely be reduced, and the Fund’s performance may be adversely affected.

Large-Capitalization Stock Risk—the stocks of large-capitalization companies are generally more mature and may not be able to reach the same levels of growth as the stocks of small- or mid-capitalization companies.

Participatory Notes Risk—an investment in participatory notes is subject to market risk. The performance results of participatory notes may not exactly replicate the performance of the underlying securities. An investment in participatory notes is also subject to counterparty risk, relating to the non-U.S. bank or broker-dealer that issues the participatory notes, and may be subject to liquidity risk.

Political Risk—changes in the general political and social environment of a country can have substantial effects on the value of investments exposed to that country.

PRC Tax Risk—the application of the tax laws and regulations of the PRC to income, including capital gains, derived from certain investments of the Fund remains unclear, and may well continue to evolve, possibly with retroactive effect. Any taxes imposed on the investments of the Fund pursuant to such laws and regulations will reduce the Fund’s overall returns.

Stock Connect Risk—trading in China A-Shares through Stock Connect is subject to sudden changes in quota limitations, application of trading suspensions, differences in trading days between the People’s Republic of China and Stock Connect, operational risk, clearing and settlement risk and regulatory and taxation risk.

Valuation Risk—the Fund may not be able to value its investments in a manner that accurately reflects their market values, and the Fund may not be able to sell an investment at a price equal to the valuation ascribed to that investment by the Fund. The valuation of the Fund’s investments involves subjective judgment. Certain securities in which the Fund may invest may be more difficult to value accurately, especially during periods of market disruptions or extreme market volatility. Incorrect valuations of the Fund’s portfolio holdings could result in the Fund’s shareholder transactions being effected at an NAV that does not accurately reflect the underlying value of the Fund’s portfolio, resulting in the dilution of shareholder interests.

Value Stock Risk—value stocks may perform differently from the market as a whole and may be undervalued by the market for a long period of time.

Also with respect to the section titled “Principal Risks” beginning on page 2, the principal risks shall appear in the following order: Market Risk; Management Risk; Focused Investment Risk; Foreign Investment Risk; Geographic Focus Risk; Currency Risk; Emerging Markets Risk; High Cash Balance Risk; High Portfolio Turnover Risk; Large-Capitalization Stock Risk; Liquidity Risk; Participatory Notes Risk; Political Risk; PRC Tax Risk; Small- and Mid-Capitalization Stock Risk; Stock Connect Risk; Valuation Risk; and Value Stock Risk.

In the section titled “Performance” on page 3, the first paragraph is deleted and replaced with the following:

The following performance information illustrates the risks of investing in the Fund by showing changes in the Fund’s performance from year to year and by showing how the Fund’s performance compares to that of two broad-based securities market indices. As always, past performance of the Fund (before and after taxes) is not an indication of how the Fund will perform in the future.

As of March 19, 2021, Veritas was appointed as subadviser to the Fund and the Fund changed its name to “AMG Veritas Asia Pacific Fund,” adopted its current investment strategies and began comparing its performance to the MSCI AC Asia Pacific ex Japan Index. The Fund’s performance information for periods prior to March 19, 2021 reflects the Fund’s investment strategy that was in effect at that time and may have been different had the Fund’s current investment strategy been in effect.

Effective February 27, 2017, outstanding Class S shares of the Fund (formerly Service Class shares, which were renamed Class S shares on October 1, 2016 (formerly Managers Class shares, which were renamed Service Class shares on April 1, 2013)) were renamed Class N shares. Effective October 1, 2016, outstanding Institutional Class shares of the Fund were renamed Class I shares.

To obtain updated performance information, please visit www.amgfunds.com or call 800.548.4539.

The Average Annual Total Returns table in the section titled “Performance” on page 3 is deleted and replaced with the following:

Average Annual Total Returns as of 12/31/20

AMG Veritas Asia Pacific Fund	1 Year			5 Years			10 Years
Class N Return Before Taxes		38.74	%		17.95	%		14.29	%
Class N Return After Taxes on Distributions		37.32	%		16.25	%		13.47	%
Class N Return After Taxes on Distributions and Sale of Fund Shares		23.89	%		14.15	%		11.87	%
Class I Return Before Taxes		39.08	%		18.24	%		14.55	%
MSCI AC Asia Pacific ex Japan Index1 (reflects no deduction for fees, expenses or taxes)		22.44	%		12.93	%		6.21	%
Russell 2000® Growth Index1 (reflects no deduction for fees, expenses or taxes)		34.63	%		16.36	%		13.48	%

¹  The MSCI AC Asia Pacific ex Japan Index replaced the Russell 2000^® Growth Index as the Fund’s benchmark on March 19, 2021 because the Investment Manager and Subadviser believe the new benchmark is more representative of the Fund’s current investment strategies.

The section titled “Portfolio Management” on page 3 is deleted and replaced with the following:

PORTFOLIO MANAGEMENT

Investment Manager

AMG Funds LLC

Subadviser

Veritas Asset Management LLP

(pursuant to an interim subadvisory agreement in anticipation of shareholder approval of a definitive subadvisory agreement)

Portfolio Manager

Ezra Sun

Head of Asia of Veritas;

Portfolio Manager of the Fund since March 2021.

In addition, effective if and when the New Subadvisory Agreement takes effect, the Summary Prospectus is amended as follows:

The sections titled “Fees and Expenses of the Fund” and “Expense Example” on page 1 are deleted and replaced with the following:

FEES AND EXPENSES OF THE FUND

The table below describes the fees and expenses that you may pay if you buy, hold and sell shares of the Fund. You may pay other fees, such as brokerage commissions and other fees to financial intermediaries, which are not reflected in the tables and examples below.

Annual Fund Operating Expenses

(expenses that you pay each year as a percentage of the value of your investment)

	Class N			Class I
Management Fee1		0.71	%		0.71	%
Distribution and Service (12b-1) Fees		None			None
Other Expenses		0.52	%		0.27	%
Total Annual Fund Operating Expenses		1.23	%		0.98	%
Fee Waiver and Expense Reimbursements2		(0.05	)%		(0.05	)%
Total Annual Fund Operating Expenses After Fee Waiver and Expense Reimbursements2		1.18	%		0.93	%

¹  Expense information has been restated to reflect current fees.

²  AMG Funds LLC (the “Investment Manager”) has contractually agreed, through at least May 1, 2023, to waive management fees and/or pay or reimburse the Fund’s expenses in order to limit Total Annual Fund Operating Expenses After Fee Waiver and Expense Reimbursements (exclusive of taxes, interest (including interest incurred in connection with bank and custody overdrafts and in connection with securities sold short), shareholder servicing fees, distribution and service (12b-1) fees, brokerage commissions and other transaction costs, dividends payable with respect to securities sold short, acquired fund fees and expenses, and extraordinary expenses) of the Fund to the annual rate of 0.93% of the Fund’s average daily net assets (this annual rate or such other annual rate that may be in effect from time to time, the “Expense Cap”), subject to later reimbursement by the Fund in certain circumstances. In general, for a period of up to 36 months after the date any amounts are paid, waived or reimbursed by the Investment Manager, the Investment Manager may recover such amounts from the Fund, provided that such repayment would not cause the Fund’s Total Annual Fund Operating Expenses After Fee Waiver and Expense Reimbursements (exclusive of the items noted in the parenthetical above) to exceed either (i) the Expense Cap in effect at the time such amounts were paid, waived or reimbursed, or (ii) the Expense Cap in effect at the time of such repayment by the Fund. The contractual expense limitation may only be terminated in the event the Investment Manager or a successor ceases to be the investment manager of the Fund or a successor fund, by mutual agreement between the Investment Manager and the AMG Funds III Board of Trustees or in the event of the Fund’s liquidation unless the Fund is reorganized or is a party to a merger in which the surviving entity is successor to the accounting and performance information of the Fund.

EXPENSE EXAMPLE

This Example will help you compare the cost of investing in the Fund to the cost of investing in other mutual funds. The Example makes certain assumptions. It assumes that you invest $10,000 as an initial investment in the Fund for the time periods indicated and then redeem all of your shares at the end of those periods. It also assumes that your investment has a 5% total return each year and the Fund’s operating expenses remain the same. The Example includes the Fund’s contractual expense limitation through May 1, 2023. Although your actual costs may be higher or lower, based on the above assumptions, your costs would be:

	1 Year		3 Years		5 Years		10 Years
Class N	$	120	$	382	$	667	$	1,481
Class I	$	95	$	304	$	533	$	1,194

PLEASE KEEP THIS SUPPLEMENT FOR FUTURE REFERENCE