A model and a sound and complete proof system for networks of processes in which component processes communicate exclusively through messages is given. The model, an extension of the trace model, can desribe both synchronous and asynchronous networks. The proof system uses temporal-logic assertions on sequences of observations - a generalization of traces. The use of observations (traces) makes the proof system simple, compositional and modular, since internal details can be hidden. The expressive power of temporal logic makes it possible to prove temporal properties (safety, liveness, precedence, etc.) in the system. The proof system is language-independent and works for both synchronous and asynchronous networks.