A generalization of Petri nets and vector addition systems, called GPN and MGPN, is introduced in this paper. Termination properties of this generalized formalism are investigated. Four subclasses of GPN’s are considered. We distinguish forward-conflict-free, backward-conflict-free, forward-concurrent-free and backward-concurrent-free GPN’s. We also study the concept of strongly connected, strongly repetitive and conservative GPN’s. The main results obtained are (i) every strongly connected, strongly repetitive and forward- (or backward-) conflict-free GPN must be conservative, and (ii) every strongly connected, conservative and forward- (or backward-) concurrent-free GPN must be strongly repetitive. Since the class of forward-conflict-free GPN’s contains properly the structures of computation graphs of Karp and Miller and marked graphs, some results appearing in these studies can be obtained as corollaries. Specialized versions of our results for the case of Petri nets are also included.