<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema"><Version>2.2.0.25</Version><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><ReportLongName>006050 - Disclosure - SHORT-TERM AND LONG-TERM DEBT</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelColumn>false</LabelColumn><CurrencyCode>USD</CurrencyCode><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName>1/1/2011 - 3/31/2011
USD ($)

USD ($) / shares
</KeyName><CurrencySymbol>$</CurrencySymbol><contextRef><ContextID>c00012</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000072020</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2011-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2011-03-31T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS><UnitProperty><UnitID>u000</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace></StandardMeasure><Scale>0</Scale></UnitProperty><UnitProperty><UnitID>u001</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema><MeasureValue>shares</MeasureValue><MeasureNamespace>xbrli</MeasureNamespace></StandardMeasure><Scale>0</Scale></UnitProperty><UnitProperty><UnitID>u002</UnitID><UnitType>Divide</UnitType><NumeratorMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace></NumeratorMeasure><DenominatorMeasure><MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema><MeasureValue>shares</MeasureValue><MeasureNamespace>xbrli</MeasureNamespace></DenominatorMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Id="1" Label="3 Months Ended" /><Label Id="2" Label="Mar. 31, 2011" /></Labels></Column></Columns><Rows><Row><Id>2</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><Level>0</Level><ElementName>gas_NotesToFinancialStatementsAbstract</ElementName><ElementPrefix>gas</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>No definition available.</ShortDefinition><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsSubReportEnd>false</IsSubReportEnd><IsCalendarTitle>false</IsCalendarTitle><IsTuple>false</IsTuple><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole /><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><NonNumericTextHeader /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>No definition available.</ElementDefenition><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>Notes to Financial Statements [Abstract]</Label></Row><Row><Id>3</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><Level>0</Level><ElementName>us-gaap_DebtDisclosureTextBlock</ElementName><ElementPrefix>us-gaap</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>No definition available.</ShortDefinition><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsSubReportEnd>false</IsSubReportEnd><IsCalendarTitle>false</IsCalendarTitle><IsTuple>false</IsTuple><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole /><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div&gt;&lt;table style="FONT-SIZE: 10pt; FONT-FAMILY: times new roman" cellspacing="0" cellpadding="0" width="100%" align="center" border="0"&gt;&lt;tr style="LINE-HEIGHT: 1.5" valign="top"&gt;&lt;td style="WIDTH: 18pt"&gt;&lt;div style="MARGIN-LEFT: 0pt; TEXT-INDENT: 0pt; MARGIN-RIGHT: 0pt"&gt;&lt;font style="DISPLAY: inline; FONT-WEIGHT: bold; FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman"&gt;5.&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td&gt;&lt;div align="left"&gt;&lt;font style="DISPLAY: inline; FONT-WEIGHT: bold; FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman"&gt;SHORT-TERM AND LONG-TERM DEBT&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;/div&gt;&lt;div style="DISPLAY: block; TEXT-INDENT: 0pt; LINE-HEIGHT: 1.5"&gt;&lt;br /&gt;&lt;/div&gt;&lt;div style="DISPLAY: block; MARGIN-LEFT: 0pt; TEXT-INDENT: 0pt; LINE-HEIGHT: 1.5; MARGIN-RIGHT: 0pt" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman"&gt;In February 2011, Nicor Gas issued $75 million First Mortgage Bonds at 2.86 percent, due in 2016 through a private placement and utilized the proceeds to retire the $75 million 6.625 percent First Mortgage Bond series which matured in February 2011.&amp;#160;&amp;#160;In determining that these bonds qualified for exemption from registration under Section 4(2) of the Securities Act of 1933, Nicor Gas relied on the facts that the bonds were offered only to a limited number of large institutional investors and each institutional investor that purchased the bonds represented&amp;#160;that it&amp;#160;was&amp;#160;purchasing the bonds for its own account and not with a view to distribute them.&amp;#160;&lt;/font&gt;&lt;/div&gt;&lt;div style="DISPLAY: block; TEXT-INDENT: 0pt; LINE-HEIGHT: 1.5"&gt;&lt;br /&gt;&lt;/div&gt;&lt;div style="DISPLAY: block; MARGIN-LEFT: 0pt; TEXT-INDENT: 0pt; LINE-HEIGHT: 1.5; MARGIN-RIGHT: 0pt" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman"&gt;In April 2011, Nicor Gas established a $400 million, 364-day revolving credit facility, expiring April 2012 to replace the $400 million, 364-day revolving credit facility, which was set to expire in April 2011.&amp;#160;&amp;#160;In April 2010, Nicor and Nicor Gas established a $600 million, three-year revolving credit facility, expiring April 2013 to replace the $600 million, five-year revolving credit facility, which was set to expire in September 2010.&amp;#160;&amp;#160;These facilities were established with major domestic and foreign banks and serve as backup for the issuance of commercial paper.&amp;#160;&amp;#160;The company had $153.7 million, $425.0 million and $228.0 million of commercial paper borrowings outstanding at March 31, 2011, December 31, 2010 and March 31, 2010, respectively.&lt;/font&gt;&lt;/div&gt;&lt;div style="DISPLAY: block; TEXT-INDENT: 0pt; LINE-HEIGHT: 1.5"&gt;&lt;br /&gt;&lt;/div&gt;&lt;div style="DISPLAY: block; MARGIN-LEFT: 0pt; TEXT-INDENT: 0pt; LINE-HEIGHT: 1.5; MARGIN-RIGHT: 0pt" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman"&gt;Nicor held forward-starting interest rate swaps with a notional totaling $90 million at March 31, 2011 and December 31, 2010 and $50 million at March 31, 2010. The swaps hedge the risk associated with the interest payments attributable to the probable issuance of long-term fixed-rate debt in 2012 intended to finance the development of a natural gas storage facility.&amp;#160;&amp;#160;Under the terms of the swaps, Nicor agrees to pay a fixed swap rate and receive a floating rate based on LIBOR.&lt;/font&gt;&lt;/div&gt;&lt;div style="DISPLAY: block; TEXT-INDENT: 0pt; LINE-HEIGHT: 1.5"&gt;&lt;br /&gt;&lt;/div&gt;&lt;div style="DISPLAY: block; MARGIN-LEFT: 0pt; TEXT-INDENT: 0pt; LINE-HEIGHT: 1.5; MARGIN-RIGHT: 0pt" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman"&gt;The company believes it is in compliance with all debt covenants.&lt;/font&gt;&lt;/div&gt;</NonNumbericText><NonNumericTextHeader>5.SHORT-TERM AND LONG-TERM DEBTIn February 2011, Nicor Gas issued $75 million First Mortgage Bonds at 2.86 percent, due in 2016 through a private placement and</NonNumericTextHeader><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>us-types:textBlockItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>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, 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 SEC
 -Name Regulation S-X (SX)
 -Number 210
 -Section 02
 -Paragraph 19, 20, 22
 -Article 5

Reference 2: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name Statement of Financial Accounting Standard (FAS)
 -Number 129
 -Paragraph 2, 4

</ElementReferences><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>SHORT-TERM AND LONG-TERM DEBT</Label></Row></Rows><Footnotes /><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows><ReportName>SHORT-TERM AND LONG-TERM DEBT</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>false</HasCustomUnits><SharesShouldBeRounded>true</SharesShouldBeRounded></InstanceReport>
