This paper addresses the problem of fault detection (FD) for networked systems with access constraints and packet dropouts. Two independent Markov chains are used to describe the sequences of channels which are available for communication at an instant and the packet dropout process, respectively. Performance indexes H∞ and H− are introduced to describe the robustness of residual against external disturbances and sensitivity of residual to faults, respectively. By using a mode-dependent fault detection filter (FDF) as residual generator, the addressed FD problem is converted into an auxiliary filter design problem with the above index constraints. A sufficient condition for the existence of the FDF is derived in terms of certain linear matrix inequalities (LMls). When these LMls are feasible, the explicit expression of the desired FDF can also be characterized. A numerical example is exploited to show the usefulness of the proposed results.