In recent years, base-isolation has become an increasingly applied structural design technique in highly seismic areas. The state-of-the-art practice is to use active or passive magneto-rheological (MR) dampers to limit the base displacement. The crucial effect of likely faults in the base-isolation system on the top superstructure requires that the resulting nonlinear hysteretic system to be monitored in real-time for possible changes in the two most important structural parameters: stiffness and damping. This paper develops a simple fault detection and diagnosis technique based on comparing the internal dynamics of the base-isolation system with those of a healthy baseline model to detect faults. Three different cases of stiffness, damping, and combined stiffness and damping faults are studied, in silico, on a realistic base-isolated structure subjected to the Loma Prieta earthquake with a passive MR damper. The simulation results show that the proposed fault detection and diagnosis algorithm is well capable of detecting the existence, determining the type, and quantifying the severity of faults in the system in real-time as the faults occur.