This paper deals with the problem of distributed fault detection for a team of multi-agent systems with linear dynamics using output observers. The proposed output observer is employed to estimate the state of virtual models based on relative outputs in order to generate a set of residual signal that are indicative of the presence of a fault. The convergence of the observer is proven for any initial condition and fault detectability conditions are defined. The proposed method ensures distributed actuator fault detection using input-output relations, where each agent is capable of detecting not only its own faults, but also those that occur in its neighbours solely by using exchanged relative outputs. Results of numerical simulations are provided to show the robustness of the proposed approach.