When both a human and a computer in a system are capable of performing the same tasks, task responsibilities may be allocated between them dynamically. This study compared two methods of human-computer communication for dynamic task allocation: explicit and model-based communication. With explicit communication the human directed the computer and the computer did not perform any actions on its own. With model-based communication the computer employed a model of the human which predicted the human's actions and the computer used this model to work on its own. Subjects performed a process monitoring task using both of these allocation methods. In addition, in half the trials subjects had knowledge of the computer's actions and in the other half they did not. The results indicated that overall system performance was always better under model-based communication, although human performance alone was better with explicit communication. In addition, overall system and human performance were higher when the human had knowledge of the computer's actions.