<?xml version="1.0" encoding="utf-8"?>
<InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema">
  <Version>1.0.0.3</Version>
  <hasSegments>false</hasSegments>
  <ReportName>New Accounting Pronouncements</ReportName>
  <RoundingOption />
  <Columns>
    <Column>
      <LabelColumn>false</LabelColumn>
      <Id>1</Id>
      <Labels>
        <Label Id="1" Label="9 Months Ended" />
        <Label Id="2" Label="Sep. 30, 2009" />
        <Label Id="4" Label="USD / shares" />
      </Labels>
      <CurrencySymbol>$</CurrencySymbol>
      <hasSegments>false</hasSegments>
      <hasScenarios>false</hasScenarios>
      <Segments />
      <Scenarios />
      <Units>
        <Unit>
          <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>
        </Unit>
        <Unit>
          <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>
        </Unit>
      </Units>
    </Column>
  </Columns>
  <Rows>
    <Row>
      <Id>2</Id>
      <Label>Notes to Financial Statements [Abstract]</Label>
      <Level>0</Level>
      <ElementName>anr_NotesToFinancialStatementsAbstract</ElementName>
      <ElementPrefix>anr</ElementPrefix>
      <IsBaseElement>false</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ElementDataType>string</ElementDataType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>true</IsAbstractGroupTitle>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsEPS>false</IsEPS>
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText />
          <NonNumericTextHeader />
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
        </Cell>
      </Cells>
      <ElementDefenition>No definition available.</ElementDefenition>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
    <Row>
      <Id>3</Id>
      <Label>New Accounting Pronouncements</Label>
      <Level>1</Level>
      <ElementName>us-gaap_ScheduleOfNewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock</ElementName>
      <ElementPrefix>us-gaap</ElementPrefix>
      <IsBaseElement>true</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ElementDataType>string</ElementDataType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>false</IsAbstractGroupTitle>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsEPS>false</IsEPS>
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText>&lt;div&gt;       &lt;div&gt;         &lt;table align="center" border="0" cellpadding="0" cellspacing="0" id="hangingindent_0" width="100%" style="FONT-SIZE: 10pt; FONT-FAMILY: times new roman; FONT-SIZE: 10pt; FONT-FAMILY: times new roman"&gt; &lt;tr 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;(2)&lt;/font&gt;&lt;/div&gt;             &lt;/td&gt;             &lt;td&gt;               &lt;div align="justify"&gt;&lt;font style="DISPLAY: inline; FONT-WEIGHT: bold; FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman"&gt;New  Accounting Pronouncements&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"&gt;&lt;br /&gt;&lt;/div&gt;       &lt;div style="DISPLAY: block; MARGIN-LEFT: 18pt; TEXT-INDENT: 0pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&lt;font style="DISPLAY: inline; FONT-SIZE: 10pt; FONT-STYLE: italic; FONT-FAMILY: Times New Roman"&gt;New  Accounting Pronouncements Adopted&lt;/font&gt;&lt;/div&gt;       &lt;div style="DISPLAY: block; MARGIN-LEFT: 0pt; TEXT-INDENT: 0pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&amp;#160;&lt;/div&gt;       &lt;div style="DISPLAY: block; MARGIN-LEFT: 0pt; TEXT-INDENT: 18pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&lt;font style="DISPLAY: inline; FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman"&gt;In June  2009, the Company adopted Accounting Standards Codification (&amp;#8220;ASC&amp;#8221;) 105, &lt;font style="DISPLAY: inline; FONT-STYLE: italic"&gt;Generally Accepted Accounting  Principles &lt;/font&gt;(&amp;#8220;ASC 105&amp;#8221;). ASC 105 defines the new hierarchy for U.S. GAAP  and supersedes all accounting standards in U.S. GAAP, aside from those issued by  the SEC. The Codification is effective for financial statements issued for  reporting periods ending after September 15, 2009.&lt;/font&gt;&lt;/div&gt;       &lt;div style="DISPLAY: block; TEXT-INDENT: 0pt"&gt;&lt;br /&gt;&lt;/div&gt;       &lt;div style="DISPLAY: block; MARGIN-LEFT: 0pt; TEXT-INDENT: 18pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&lt;font style="DISPLAY: inline; FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman"&gt;In August  2009, the Financial Accounting Standards Board (&amp;#8220;FASB&amp;#8221;) issued ASC 820, &lt;font style="DISPLAY: inline; FONT-STYLE: italic"&gt;Fair Value Measurements and  Disclosures &amp;#8211; Measuring Liabilities at Fair Value&lt;/font&gt;.&amp;#160;&amp;#160;The new  guidance establishes valuation techniques in circumstances in which a quoted  price in an active market for the identical liability is not  available.&amp;#160;&amp;#160;Additionally, it clarifies appropriate valuation  techniques when restrictions exist that prevent the transfer of liabilities  measured at fair value.&amp;#160;&amp;#160;Finally, it provides further guidance on the  classification of liabilities measured at fair value within the fair value  hierarchy.&amp;#160;&amp;#160;The new guidance is effective for interim periods ending  after August 26, 2009.&amp;#160;&amp;#160;The adoption of the guidance did not have an  impact on the Company&amp;#8217;s results of operations or financial  position.&lt;/font&gt;&lt;/div&gt;       &lt;div style="DISPLAY: block; TEXT-INDENT: 0pt"&gt;&lt;br /&gt;&lt;/div&gt;       &lt;div style="DISPLAY: block; MARGIN-LEFT: 18pt; TEXT-INDENT: 0pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&lt;font style="DISPLAY: inline; FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman"&gt;&lt;font style="DISPLAY: inline; FONT-SIZE: 10pt; FONT-STYLE: italic"&gt;New Accounting  Pronouncements Issued and not yet Adopted&lt;/font&gt;&lt;/font&gt;&lt;/div&gt;       &lt;div style="DISPLAY: block; TEXT-INDENT: 0pt"&gt;&lt;br /&gt;&lt;/div&gt;       &lt;div style="DISPLAY: block; MARGIN-LEFT: 0pt; TEXT-INDENT: 18pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&lt;font style="DISPLAY: inline; FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman"&gt;In June  2009, the FASB issued Statement of Financial Accounting Standards &amp;#8220;SFAS&amp;#8221; No.  166, &lt;font style="DISPLAY: inline; FONT-STYLE: italic"&gt;Accounting for Transfers  of Financial Assets &amp;#8211; an amendment of FASB Statement No. 140 &lt;/font&gt;(&amp;#8220;SFAS  166&amp;#8221;)&lt;font style="DISPLAY: inline; FONT-STYLE: italic"&gt;&amp;#160;&lt;/font&gt;(which has  been incorporated into ASC 860&lt;font style="DISPLAY: inline; FONT-STYLE: italic"&gt;)&lt;/font&gt;.&amp;#160;&amp;#160;SFAS 166 amends  the criteria for a transfer of a financial asset to be accounted for as a sale,  redefines a participating interest for transfers of portions of financial  assets, eliminates the qualifying special-purpose entity concept and provides  for new disclosures. SFAS 166 is effective for fiscal years beginning after  November 15, 2009, and its adoption is not expected to affect the Company&amp;#8217;s  financial position or results of operations.&lt;/font&gt;&lt;/div&gt;       &lt;div style="DISPLAY: block; TEXT-INDENT: 0pt"&gt;&lt;br /&gt;&lt;/div&gt;       &lt;div style="DISPLAY: block; MARGIN-LEFT: 0pt; TEXT-INDENT: 18pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&lt;font style="DISPLAY: inline; FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman"&gt;ASC  715-20, &lt;font style="DISPLAY: inline; FONT-STYLE: italic"&gt;Defined Benefit Plans  - General &lt;/font&gt;(&amp;#8220;ASC 715-20&amp;#8221;). ASC 715-20 provides guidance on an employer&amp;#8217;s  disclosures about plan assets of a defined benefit pension or other  postretirement plan. The additional disclosure requirements under this ASC  include expanded disclosures about an entity&amp;#8217;s investment policies and  strategies, the categories of plan assets, and concentrations of credit risk and  fair value measurements of plan assets. ASC 715-20 will be effective for fiscal  years ending after December 15, 2009. The implementation of this standard will  have no impact on the amounts recorded in the Company&amp;#8217;s consolidated financial  statements. The Company will include the additional disclosures in the notes to  the Company&amp;#8217;s consolidated financial statements for the year ending December 31,  2009.&lt;/font&gt;&lt;/div&gt;&lt;br /&gt;&lt;/div&gt;</NonNumbericText>
          <NonNumericTextHeader>(2)                                         New  Accounting Pronouncements                                             New  Accounting Pronouncements Adopted  </NonNumericTextHeader>
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
        </Cell>
      </Cells>
      <ElementDefenition>No definition available.</ElementDefenition>
      <ElementReferences>No authoritative reference available.</ElementReferences>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
  </Rows>
  <Footnotes />
  <ComparabilityReport>false</ComparabilityReport>
  <NumberOfCols>1</NumberOfCols>
  <NumberOfRows>2</NumberOfRows>
  <HasScenarios>false</HasScenarios>
  <MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel>
  <SharesRoundingLevel>UnKnown</SharesRoundingLevel>
  <PerShareRoundingLevel>UnKnown</PerShareRoundingLevel>
  <HasPureData>false</HasPureData>
  <SharesShouldBeRounded>true</SharesShouldBeRounded>
</InstanceReport>
