We present a process algebraic intruder model for verifying a class of liveness properties of security protocols. For this class, the proposed intruder model is proved to be equivalent to a Dolev-Yao intruder that does not delay indefinitely the delivery of messages. In order to prove the equivalence, we formalize the resilient communication channels assumption. As an application of the proposed intruder model, formal verification of fair exchange protocols is discussed.