Multi-agent systems (MASs) have a wide range of applications in many industrial areas. The agents often collaborate and coordinate their actions through the exchange of information via communication networks. However, faults and cyber-attacks on a single agent may propagate to other agents via information interaction rapidly and thus could lead to severe degradation of performance and even the complete breakdown of MASs. Motivated by the requirements, this dissertation is dedicated to developing distributed observer-based detection schemes for faults and cyber-attacks of MASs. Firstly, depending on large-scale time-varying sensor networks, a distributed H₂ observer is designed and implemented in a recursive form, to improve the accuracy of state estimation and small fault detection for a target agent. Secondly, to detect the interruption of MASs caused by denial-of-service (DoS) attacks, a detection scheme combining a generalized likelihood ratio (GLR) approach and an offline statistical threshold training method is proposed. Finally, we have addressed the distributed detection problem for cooperative fault tolerant control (FTC) of MASs under stealthy integrity cyber-attacks. A distributed encrypted detection scheme with a switching system is developed to determine whether the reference signals transmitted between neighboring agents are secure from stealthy attacks. The two advantages of the scheme are non-affection on control performance and preventing adversaries from gaining insights into MASs. To validate the effectiveness and feasibility of the schemes, we have presented a range of simulation investigations and practical experiments involving a two-robot system.