Capital constraints were not considered in the classical modes.  How duopoly firms with capital constraints withdraw from an industry whose demands are declining was studied. Basic mode is proposed for du-oligarch firms’ strategic withdrawing.  Introducing capital constraints, the analysis was done of how the firms’ capital strengths influence the opportunities and orders of their withdraws.  The model shows the firm with “long purse” may find it optimal to stay in the market despite making temporary losses to outlast its rival in the war of attrition. The optimal strategy for that monopoly firms customarily is to persist in the market, differing from the traditional models in which the firms lacking the strategic advantages would withdraw. 