<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>1130 - Disclosure - DEBT</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>D2013Q2YTD</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000883569</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2012-12-30T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-29T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 29, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>us-gaap_DebtDisclosureAbstract</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>DEBT</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_DebtDisclosureTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="D2013Q2YTD" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="font-size:10.0pt;font-family:Times New Roman;"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&lt;b&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt; FONT-WEIGHT: bold;" size="2"&gt;13. DEBT&lt;/font&gt;&lt;/b&gt;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 24.5pt; MARGIN: 0in 0in 0pt;"&gt;&lt;b&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt; FONT-WEIGHT: bold;" size="2"&gt;Short Term Foreign-Based Activity.&lt;/font&gt;&lt;/b&gt;&lt;font style="FONT-SIZE: 10pt;" size="2"&gt;&amp;#160; Due to the deconsolidation of STC during the Second Quarter, the 1.1 million Swiss Franc note entered into by STC on October&amp;#160;31, 2012 is no longer recognized on the Company&amp;#8217;s condensed consolidated balance sheets as of June&amp;#160;29, 2013. See &amp;#8220;Note 2-Acquisitions, Divestiture and Goodwill&amp;#8221; for additional disclosures on the deconsolidation of STC.&lt;/font&gt;&lt;/p&gt;
&lt;p style="TEXT-ALIGN: center; MARGIN: 0in 0in 0pt;" align="center"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 24.5pt; MARGIN: 0in 0in 0pt;"&gt;&lt;b&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt; FONT-WEIGHT: bold;" size="2"&gt;Long Term U.S.-Based Activity&lt;/font&gt;&lt;/b&gt;&lt;font style="FONT-SIZE: 10pt;" size="2"&gt;.&amp;#160; On May&amp;#160;17, 2013, the Company and certain of its subsidiaries entered into a five year Credit Agreement (the &amp;#8220;Credit Agreement&amp;#8221;) with (i)&amp;#160;the lenders party thereto, (ii)&amp;#160;Wells Fargo Bank, National Association (&amp;#8220;Wells Fargo&amp;#8221;), as administrative agent, swingline lender and issuing lender, (iii)&amp;#160;Bank of America, N.A. and JPMorgan Chase Bank, N.A., as syndication agents, (iv)&amp;#160;HSBC Bank USA, National Association and Fifth Third Bank, as documentation agents, and (v)&amp;#160;Wells Fargo Securities, LLC, Merrill Lynch, Pierce, Fenner&amp;#160;&amp;amp; Smith Incorporated and J.P. Morgan Securities LLC, as joint lead arrangers and bookrunners.&amp;#160; The Credit Agreement provides for revolving credit loans in the amount of $750 million (the &amp;#8220;Revolver&amp;#8221;), a swingline subfacility up to $20 million, an up to $10 million subfacility for letters of credit, and a term loan in the amount of $250 million (the &amp;#8220;Term Loan&amp;#8221;).&amp;#160;The Credit Agreement expires and is due and payable on May&amp;#160;17, 2018. The Credit Agreement is guaranteed by all direct and indirect material domestic subsidiaries of the Company and is secured by 65% of the outstanding voting capital stock and 100% of the non-voting capital stock of the following foreign subsidiaries of the Company: Fossil Europe&amp;#160;B.V., Swiss Technology Holding&amp;#160;GmbH and Fossil (East) Limited. In connection with entering into the Credit Agreement, the Company paid upfront fees of approximately $4.8 million, which are being amortized over the life of the Credit Agreement.&lt;/font&gt;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 24.5pt; MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;Amounts outstanding under the Revolver and Term Loan bear interest at the Company&amp;#8217;s option of (i)&amp;#160;the base rate (defined as the higher of (a)&amp;#160;the prime rate publicly announced by Wells Fargo (3.75% at the end of the Second Quarter), (b)&amp;#160;the federal funds rate plus 0.5% and (c)&amp;#160;the London Interbank Offer Rate (&amp;#8220;LIBOR&amp;#8221;) (0.2% at the end of the Second Quarter) for an interest period of one month plus 1.0%) plus the base rate applicable margin (which varies based upon the Company&amp;#8217;s consolidated leverage ratio (the &amp;#8220;Ratio&amp;#8221;) from 0.25% if the Ratio is less than 1.00 to 1.00, to 1.00% if the Ratio is greater than or equal to 2.00 to 1.00) or (ii)&amp;#160;the LIBOR rate (defined as the quotient obtained by dividing (a)&amp;#160;LIBOR by (b)&amp;#160;1.00 minus the Eurodollar reserve percentage) plus the LIBOR rate applicable margin (which varies based upon the Ratio from 1.25% if the Ratio is less than 1.00 to 1.00, to 2.00% if the Ratio is greater than or equal to 2.00 to 1.00). Amounts outstanding under the swingline loan under the Credit Agreement or upon any drawing under a letter of credit bear interest at the base rate plus the base rate applicable margin. Interest based upon the base rate is payable quarterly in arrears. Interest based upon the LIBOR rate is payable either monthly or quarterly in arrears, depending on the interest period selected by the Company. The Revolver also includes a commitment fee ranging from 0.20% to 0.35% for any amounts not drawn under the Revolver.&lt;/font&gt;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;The Credit Agreement replaced a credit agreement dated as of December&amp;#160;17, 2010, as amended, by and among the Company and certain of its subsidiaries, Wells Fargo Bank, National Association, as administrative agent, swingline lender and issuing lender, Wells Fargo Securities, LLC, as sole lead arranger and sole book manager and Bank of America, N.A., as lender, which was scheduled to mature on December&amp;#160;17, 2014 (the &amp;#8220;Prior Credit Agreement&amp;#8221;). The Company incurred approximately $0.5&amp;#160;million and $1.2 million of interest expense related to the Prior Credit Agreement during the Second Quarter and Year To Date Period, respectively.&amp;#160; Additionally, during the Year To Date Period, the Company had total borrowings of $346.5 million and repayments of $411.5 million, inclusive of the final payment of $248.0 million. The Company incurred approximately $0.7 million of interest expense related to the Prior Credit Agreement during the Prior Year Quarter and Prior Year YTD Period. On May&amp;#160;17, 2013, the entire amount outstanding under the Prior Credit Agreement was repaid using funds borrowed under the Credit Agreement. No penalties or other early termination fees were incurred in connection with the termination of the Prior Credit Agreement.&lt;/font&gt;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;Loans under the Credit Agreement may be prepaid, in whole or in part, at the option of the Company, in minimum principal amounts of $2.0&amp;#160;million or increments of $1.0&amp;#160;million in excess thereof with respect to a base rate loan under the Revolver, $5.0&amp;#160;million or increments of $1.0&amp;#160;million in excess thereof with respect to a LIBOR rate loan under the Revolver and Term Loan, and $100,000 or increments of $100,000 in excess thereof with respect to a swingline loan. Loans under the Credit Agreement must be repaid with the net proceeds of certain asset sales, insurance and condemnation events. The Company may permanently reduce the revolving credit commitment at any time, in whole or in part, without premium or penalty, in a minimum aggregate principal amount of not less than $3.0&amp;#160;million or increments of $1.0&amp;#160;million in excess thereof.&lt;/font&gt;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;Wells Fargo can accelerate the repayment obligation upon the occurrence of an event of default, including the failure to pay principal or interest, a material inaccuracy of a representation or warranty, violation of covenants, cross-default, change in control, bankruptcy events, failure of a loan document provision, certain ERISA events and material judgments.&lt;/font&gt;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;During the Year To Date Period, the Company had borrowings of $250.0 million under the Term Loan which was used to pay off amounts outstanding under the Prior Credit Agreement and pay upfront fees related to the Credit Agreement. During the Year To Date Period, the Company also had borrowings of $80.0 million under the Revolver which was used primarily to fund common stock repurchases. As of June&amp;#160;29, 2013, $250.0 million and $80.0 million were outstanding under the Term Loan and the Revolver, respectively.&amp;#160; Amounts available under the Revolver are reduced by any amounts outstanding under standby letters of credit. As of June&amp;#160;29, 2013, the Company had available borrowings of approximately $669.0&amp;#160;million under the Revolver. The Company incurred approximately $0.5&amp;#160;million of interest expense related to the Term Loan during the Second Quarter and Year To Date Period. The Company incurred approximately $15,000 of interest expense related to the Revolver during the Second Quarter and Year To Date Period.&lt;/font&gt;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;Financial covenants in the Credit Agreement require the Company to maintain (i)&amp;#160;a consolidated leverage ratio no greater than 2.50 to 1.00, (ii)&amp;#160;a consolidated interest coverage ratio no less than 3.50 to 1.00, and (iii)&amp;#160;maximum capital expenditures not in excess of (x)&amp;#160;$200.0 million from the closing through the fiscal year ending 2013 and during each of fiscal years 2014 and 2015 and (y)&amp;#160;$250.0 million during each fiscal year thereafter, subject to certain adjustments. The Credit Agreement contains representations, warranties, covenants, events of default and indemnities that are customary for agreements of this type. The Company was in compliance with all covenants in the Credit Agreement as of June&amp;#160;29, 2013 and during the Second Quarter.&lt;/font&gt;&lt;/p&gt;
&lt;/div&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure for information about short-term and long-term debt arrangements, which includes amounts of borrowings under each line of credit, note payable, commercial paper issue, bonds indenture, debenture issue, own-share lending arrangements and any other contractual agreement to repay funds, and about the underlying arrangements, rationale for a classification as long-term, including repayment terms, interest rates, collateral provided, restrictions on use of assets and activities, whether or not in compliance with debt covenants, and other matters important to users of the financial statements, such as the effects of refinancing and noncompliance with debt covenants.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 505

 -SubTopic 10

 -Section 50

 -Paragraph 3

 -URI http://asc.fasb.org/extlink&amp;oid=6928386&amp;loc=d3e21475-112644



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 02

 -Paragraph 19, 20, 22

 -Article 5



Reference 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Statement of Financial Accounting Standard (FAS)

 -Number 129

 -Paragraph 2, 4

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



Reference 4: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 210

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.5-02.19,20,22)

 -URI http://asc.fasb.org/extlink&amp;oid=6877327&amp;loc=d3e13212-122682



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>DEBT</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>DEBT</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.fossil.com/role/DisclosureDebt</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
