Abstract. This paper shows how to define Petri nets through recursive equations. It specifically addresses this problem within the context of the {it box algebra}, a model of concurrent computation which combines Petri nets and standard process algebras. The paper presents a detailed investigation of the solvability of recursive equations on nets in what is arguably the most general setting. For it allows an infinite number of possibly unguarded equations, each equation possibly involving infinitely many recursion variables. The main result is that by using a suitable partially ordered domain of nets, it is always possible to solve a system of equations by constructing the limit of a chain of successive approximations.