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The aim of this note is twofold. Firstly, it shows that the undecidability result for bisimilarity in [Theor. Comput. Sci. 148 (1995) 281-301] can be immediately extended for the whole range of equivalences (and preorders) on labelled Petri nets. Secondly, it shows that restricting our attention to nets with ÿnite reachable space, the respective (decidable) problems are nonprimitive recursive; this approach also applies to Mayr and Meyer's result [J. ACM 28 (1981) 561-576] for the reachability set equality, yielding a more direct proof.doi:10.1016/s0304-3975(00)00100-6 fatcat:a3jdzuu5vba6pljcpfe65fiv3u