Abstract : This paper describes a method to verify safety properties of parameterized networks of processes defined by network grammars. The method is based on the construction of a network invariant, defined as a fixpoint. We propose heuristics, based on Cousot's extrapolation techniques (widening), which often allow suitable invariants to be automatically constructed. We successively consider linear and binary tree networks. These techniques have been implemented in a verification tool, and several non-trivial examples are presented.