In the paper the task of concurrent analysis of a Petri net is considered. A Petri net is given, and several processes able to simulate transition firings. The methods of analysis described in this paper are based on the original approach to net decomposition and oriented for the sc-called operational nets and a class of cyclic Petri nets. The methods analyze the nets by reduced state space constructing; both their sequential and parallel versions are described. Also the algorithm of decomposition oriented to concurrent analysis is described. The suggested methods of analysis can be implemented as a multithread application.