Summary: Process algebraic techniques for distributed systems are increasingly being targeted at identifying abstractions that are adequate for both high-level programming and specification and security analysis and verification. Drawing on our earlier work, we investigate the expressive power of a core set of security and network abstractions that provide high-level primitives for specifying the honest principals in a network, while at the same time enabling an analysis of the network-level adversarial attacks that may be mounted by an intruder. We analyse various bisimulation equivalences for security that arise from endowing the intruder with: (i) different adversarial capabilities; and (ii) increasingly powerful control over the interaction among the distributed principals of a network. By comparing the relative strength of the bisimulation equivalences, we obtain a direct measure of the intruder’s discriminating power, and hence of the expressiveness of the corresponding intruder model.