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          forth the following indicia or "badges" of fraud:  (1)                      
          Understatement of income; (2) maintenance of inadequate records;            
          (3) failure to file tax returns; (4) implausible or inconsistent            
          explanations of behavior; (5) concealment of assets; and (6)                
          failure to cooperate with tax authorities.  The Court of Appeals            
          also stated that the existence of the following facts                       
          additionally supported a finding of fraudulent intent:  (1)                 
          Dealing in cash to avoid scrutiny of finances; and (2) failing to           
          make estimated tax payments.  See Bradford v. Commissioner at               
          308.                                                                        
                    1.  Evidence of Fraud--Failure to File Tax Returns                
               The parties have stipulated that petitioner did not file               
          income tax returns for any of the years in issue (1989-94).  The            
          parties have also stipulated that petitioner did not file returns           
          for any of the years 1978-88.                                               
               Although the failure to file a return is evidence of fraud,            
          we have often said that without more it is insufficient to prove            
          fraud.  This is because a finding of fraud requires proof of some           
          convincing affirmative act or indication of the taxpayer's                  
          fraudulent intent.  See Bagby v. Commissioner, 102 T.C. 596, 607-           
          608 (1994); Kotmair v. Commissioner, 86 T.C. 1253, 1261 (1986).             
          Other courts have stated the law similarly.  See, e.g., Zell v.             
          Commissioner, 763 F.2d 1139, 1143 (10th Cir. 1985), affg. T.C.              
          Memo. 1984-152.  However, the failure to file numerous returns              
          over an extended period of time is, under certain circumstances,            
          persuasive evidence of fraud.  See Stoltzfus v. United States,              
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