<?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>116 - Disclosure - Related Party Transactions</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>eol_PE10315---1310-Q0011_STD_181_20130630_0</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001069308</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</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. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>4</Level><ElementName>us-gaap_RelatedPartyTransactionsDisclosureTextBlock</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_PE10315---1310-Q0011_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 style="DISPLAY: inline; FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt"&gt;
&lt;div style="TEXT-INDENT: 0pt; DISPLAY: block; MARGIN-LEFT: 0pt; MARGIN-RIGHT: 0pt" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt; FONT-WEIGHT: bold"&gt;
Note 8.&amp;#xA0;&amp;#xA0;Related Party Transactions&lt;/font&gt;&lt;/div&gt;
&lt;div style="TEXT-INDENT: 0pt; DISPLAY: block"&gt;&lt;br /&gt;&lt;/div&gt;
&lt;div style="TEXT-INDENT: 18pt; DISPLAY: block; MARGIN-LEFT: 0pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt"&gt;Investors
in the January 2013 Notes offering included one member of
Opexa&amp;#x2019;s Board of Directors who was issued a note with a
principal amount of $100,000 (see Note 7).&lt;/font&gt;&lt;/div&gt;
&lt;div style="TEXT-INDENT: 0pt; DISPLAY: block"&gt;&lt;br /&gt;&lt;/div&gt;
&lt;div style="TEXT-INDENT: 18pt; DISPLAY: block; MARGIN-LEFT: 0pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt"&gt;The
following table provides a summary of the changes in convertible
debt &amp;#x2013; related parties, net of unamortized discount, during
the quarter ended June 30, 2013:&lt;/font&gt;&lt;/div&gt;
&lt;div style="TEXT-INDENT: 0pt; DISPLAY: block"&gt;&lt;br /&gt;&lt;/div&gt;
&lt;div align="center"&gt;
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&lt;td valign="bottom" width="88%" align="left"&gt;
&lt;div style="TEXT-INDENT: -18pt; DISPLAY: block; MARGIN-LEFT: 18pt; MARGIN-RIGHT: 0pt" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;Balance
at December 31, 2012&lt;/font&gt;&lt;/div&gt;
&lt;/td&gt;
&lt;td valign="bottom" width="1%" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="TEXT-ALIGN: left" valign="bottom" width="1%"&gt;
&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;
$&lt;/font&gt;&lt;/td&gt;
&lt;td style="TEXT-ALIGN: right" valign="bottom" width="9%"&gt;
&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;58,105&lt;/font&gt;&lt;/td&gt;
&lt;td style="TEXT-ALIGN: left" valign="bottom" width="1%" nowrap="nowrap"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr bgcolor="white"&gt;
&lt;td valign="bottom" width="88%" align="left"&gt;
&lt;div style="TEXT-INDENT: -18pt; DISPLAY: block; MARGIN-LEFT: 18pt; MARGIN-RIGHT: 0pt" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;January
2013 Notes, face value&lt;/font&gt;&lt;/div&gt;
&lt;/td&gt;
&lt;td valign="bottom" width="1%" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="TEXT-ALIGN: left" valign="bottom" width="1%"&gt;
&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;
&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="TEXT-ALIGN: right" valign="bottom" width="9%"&gt;
&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;100,000&lt;/font&gt;&lt;/td&gt;
&lt;td style="TEXT-ALIGN: left" valign="bottom" width="1%" nowrap="nowrap"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
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&lt;td valign="bottom" width="88%" align="left"&gt;
&lt;div style="TEXT-INDENT: -18pt; DISPLAY: block; MARGIN-LEFT: 18pt; MARGIN-RIGHT: 0pt" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;Discount
on beneficial conversion feature of January 2013 Notes at
issuance&lt;/font&gt;&lt;/div&gt;
&lt;/td&gt;
&lt;td valign="bottom" width="1%" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="TEXT-ALIGN: left" valign="bottom" width="1%"&gt;
&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;
&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="TEXT-ALIGN: right" valign="bottom" width="9%"&gt;
&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;(21,820&lt;/font&gt;&lt;/td&gt;
&lt;td style="TEXT-ALIGN: left" valign="bottom" width="1%" nowrap="nowrap"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;)&lt;/font&gt;&lt;/td&gt;
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&lt;td valign="bottom" width="88%" align="left"&gt;
&lt;div style="TEXT-INDENT: -18pt; DISPLAY: block; MARGIN-LEFT: 18pt; MARGIN-RIGHT: 0pt" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;Discount
on fair value of Series J warrant liability at
issuance&lt;/font&gt;&lt;/div&gt;
&lt;/td&gt;
&lt;td valign="bottom" width="1%" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="TEXT-ALIGN: left" valign="bottom" width="1%"&gt;
&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;
&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="TEXT-ALIGN: right" valign="bottom" width="9%"&gt;
&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;(30,149&lt;/font&gt;&lt;/td&gt;
&lt;td style="TEXT-ALIGN: left" valign="bottom" width="1%" nowrap="nowrap"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;)&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
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&lt;td valign="bottom" width="88%" align="left"&gt;
&lt;div style="TEXT-INDENT: -18pt; DISPLAY: block; MARGIN-LEFT: 18pt; MARGIN-RIGHT: 0pt" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;Repayment
of January 23, 2013 Notes&lt;/font&gt;&lt;/div&gt;
&lt;/td&gt;
&lt;td valign="bottom" width="1%" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="TEXT-ALIGN: left" valign="bottom" width="1%"&gt;
&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;
&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="TEXT-ALIGN: right" valign="bottom" width="9%"&gt;
&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;(100,000&lt;/font&gt;&lt;/td&gt;
&lt;td style="TEXT-ALIGN: left" valign="bottom" width="1%" nowrap="nowrap"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;)&lt;/font&gt;&lt;/td&gt;
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of debt discount to interest expense through June 30,
2013&lt;/font&gt;&lt;/div&gt;
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&lt;td style="PADDING-BOTTOM: 2px" valign="bottom" width="1%" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="BORDER-BOTTOM: black 2px solid; TEXT-ALIGN: left" valign="bottom" width="1%"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="BORDER-BOTTOM: black 2px solid; TEXT-ALIGN: right" valign="bottom" width="9%"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;97,105&lt;/font&gt;&lt;/td&gt;
&lt;td style="BORDER-BOTTOM: black 2px solid; TEXT-ALIGN: left" valign="bottom" width="1%" nowrap="nowrap"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
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&lt;div style="TEXT-INDENT: -18pt; DISPLAY: block; MARGIN-LEFT: 18pt; MARGIN-RIGHT: 0pt" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;Balance
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&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 4px" valign="bottom" width="1%" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="BORDER-BOTTOM: black 4px double; TEXT-ALIGN: left" valign="bottom" width="1%"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: times new roman; FONT-SIZE: 10pt"&gt;$&lt;/font&gt;&lt;/td&gt;
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&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
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&lt;/div&gt;
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