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In this paper, the Extended Strong Asymmetric Choice Nets Ⅱ (ESACN Ⅱ), a subclass of Asymmetric Choice Nets (ACN) including Extended Free Choice Nets (EFCN) and Strong Asymmetric Choice Nets Ⅱ (SACN Ⅱ), is presented. A necessary and sufficient condition for liveness of ESACN Ⅱ is proposed. Moreover, a criterion is introduced, which is necessary and sufficient for judgement of liveness and boundedness of ESACN Ⅱ. Meanwhile a polynomial time algorithm is given to decide liveness and boundedness for ESACN Ⅱ.