<?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>110 - Disclosure - ASSET RETIREMENT OBLIGATIONS</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

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</LabelSeparator><Level>1</Level><ElementName>us-gaap_AssetRetirementObligationDisclosureAbstract</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>Asset Retirement Obligation Disclosure [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_AssetRetirementObligationDisclosureTextBlock</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="eol_PE23789---1310-Q0005_STD_181_20130630_0" UnitID=""><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="BORDER-COLLAPSE: collapse" border="0" cellspacing="0" cellpadding="0" width="100%"&gt;
&lt;tr&gt;
&lt;td valign="top" width="4%" align="left"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&lt;b&gt;4.&lt;/b&gt;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="top" align="left"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&lt;b&gt;ASSET RETIREMENT
OBLIGATIONS&lt;/b&gt;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;p style="MARGIN-TOP: 6px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;The following
table describes the changes to the Partnership&amp;#x2019;s asset
retirement obligation liability for the first six months of
2013:&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px; FONT-SIZE: 12px"&gt;
&amp;#xA0;&lt;/p&gt;
&lt;table style="BORDER-COLLAPSE: collapse" border="0" cellspacing="0" cellpadding="0" width="68%" align="center"&gt;
&lt;tr&gt;
&lt;td width="85%"&gt;&lt;/td&gt;
&lt;td valign="bottom" width="6%"&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr bgcolor="#CCEEFF"&gt;
&lt;td valign="top"&gt;
&lt;p style="TEXT-INDENT: -1em; MARGIN-LEFT: 1em"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Asset retirement obligation
at December&amp;#xA0;31, 2012&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;2,161,807&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td valign="top"&gt;
&lt;p style="TEXT-INDENT: -1em; MARGIN-LEFT: 1em"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Accretion
expense&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;63,504&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr bgcolor="#CCEEFF"&gt;
&lt;td valign="top"&gt;
&lt;p style="TEXT-INDENT: -1em; MARGIN-LEFT: 1em"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Liabilities
settled&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;(195,851&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;)&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td valign="top"&gt;
&lt;p style="TEXT-INDENT: -1em; MARGIN-LEFT: 1em"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Revisions in estimated
liabilities&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;173,267&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr style="FONT-SIZE: 1px"&gt;
&lt;td valign="bottom"&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&amp;#xA0;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 1px solid"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 1px solid"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td&gt;&amp;#xA0;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr bgcolor="#CCEEFF"&gt;
&lt;td valign="top"&gt;
&lt;p style="TEXT-INDENT: -1em; MARGIN-LEFT: 1em"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Asset retirement obligation
at June&amp;#xA0;30, 2013&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;2,202,727&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr style="FONT-SIZE: 1px"&gt;
&lt;td valign="bottom"&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&amp;#xA0;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 3px double"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 3px double"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td&gt;&amp;#xA0;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&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 an asset retirement obligation and the associated long-lived asset. An asset retirement obligation is a legal obligation associated with the disposal or retirement from service of a tangible long-lived asset that results from the acquisition, construction or development, or the normal operations of a long-lived asset, except for certain obligations of lessees.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

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