This paper presents a class of multi-agent systems where the state of each agent is driven by its own local protocol, and by exogenous time-varying input signal. These inputs may represent agent dynamics and, in presence of unreliable communication medium, transmission noise.We consider multi-agent systems operating over asynchronous networks. Examples of such systems are message-passing systems in which agents don't share a global clock and communicate only by sending and receiving messages that may be lost, delayed arbitrarily, and delivered out of order. We present conditions on the protocols and input signals that ensure zero or bounded steadystate error over asynchronous communication networks. We discuss two specific examples and apply our general results to them. These systems are an iterative group-based protocol for average consensus of time-varying quantities, and a scheme for spatial pattern configuration, where mobile agents communicate via message-passing.