The RV reducer is a critical component of industrial robots, and studying the signal characteristics related with its gear faults is of significant importance for fault diagnosis and health maintenance. Gear time-varying meshing stiffness is a key factor influencing the dynamic response of gear systems. This study first analyzes the time-varying meshing stiffness of planetary and cycloidal-pin stages under normal, planet gear fault, and cycloidal gear fault conditions. And the time-varying meshing stiffness is used as internal excitation for the pure torsional dynamic model of the RV reducer to generate instantaneous angular speed (IAS) simulation signals. The dynamic behaviors and signal characteristics corresponding to different gear faults are analyzed and revealed. The results show that planet and cycloidal gear faults exhibit the same fault period. However, due to the higher contact ratio of cycloidal gear compared to involute gear, the abnormal signal jitter caused by cycloidal gear faults is greater in range, whereas the jitter caused by planet gear faults is smaller. In the order spectrum, planet gear fault result in significant fault-related sideband harmonics around the planetary-stage meshing order, while cycloidal gear faults produce prominent fault-related sideband harmonics around the cycloidal-pin meshing orders. These signal characteristics can effectively distinguish between planet and cycloidal gear faults. Finally, experimental verification was conducted using an RV reducer test rig. IAS under normal, planet gear fault, and cycloidal gear fault conditions were collected using a built-in encoder of the servo motor. Analysis of the experimental signals confirmed the distinct dynamic response behaviors and characteristics corresponding to different gear faults, enabling effective fault identification for planetary and cycloidal gears.