It is well known that the processes of a Petri net represent its true concurrent behaviour [11]. For the safe nets, the processes can
be replaced by traces on firing sequences [2, 3]. In the present paper we generalize this result for a special class of nets which is strictly larger than the class of safe nets. Namely, we prove that the processes of such nets can be replaced by some semi-traces on firing sequences. We also show that for a net in which every final process has a global observation, some set of its final semi-traces on firing sequences forms a prime event structure, and hence its induced finitary algebraic domain is equivalent to the one generated by the set of processes.