Abstract: Synchronous composition is an effective method for studying properties of complex Petri nets. A class of synchronous composition nets, the T composition Petri net made by composition of nets via a set of transitions,is introduced.Based on the notion of order pairs of firing transitions and the reachable marking graph of Petri nets,a set of necessary and sufficient conditions are obtained,which can be used to decide liveness and fairness of T composition Petri net.These results are useful for studying dynamic characters of complex Petri nets.