The problem on liveness judgementis stillopen in Petrinets．The paper studies liveness on Asym－metric Choice nets（AC nets）by structure analysis theory．Firstly，some known results on liveness are dis－cussed．Then a sufficient condition by S－invariant for the liveness ofACnets is presented and the correspondingpolynomial－time algorithm is got．Finally a simple necessary－and－sufficientcondition on monotonicity ofboundedACnets is presented．