In recent years, numerous distributed algorithms have been proposed which, when executed by a team of dynamic agents, result in the completion of a joint task. However, for any such algorithm to be practical, one should be able to guarantee that the task is still satisfactorily executed even when agents fail to communicate with others or to perform their designated actions correctly. In this paper, we present a concept of robustness which is well-suited for general distributed algorithms for teams of dynamic agents. Our definition extends a similar notion introduced in the distributed computation literature for consensus problems. We illustrate the definition by considering a variety of algorithms.