Abstract: As an efficient test method for studying the dynamic performance of structures subjected to dynamic loadings, the real-time substructure test (RTST) has been widely investigated and accepted by scholars all over the world. It is necessary to prevent the experiment form instability using stability analysis in RTST. The state-of-art of stability analysis methods for RTST is introduced. Taking the single degree of freedom (SDOF) RTST as an example, the system is discretized using z-transform. Then, the numerical integration algorithm, CR algorithm, is introduced into the closed-loop sytem to obtain the discrete transfer function of the system. The stability of the system is determined by the pole location of the transfer function. At the same time, the stable region of RTST is also obtained. The influence of the partition method of substructures and of the damping ratio on the stability of RTST is studied using the discrete method proposed. And the results of the two methods, the proposed method and the continuous stability analysis method, are compared. The accuracy and reliability of the method is proved by numerical simulation and by the experiment. The results show that the mass ratio and stiffness ratio play critical roles in the stability of the RTST system. The stability of RTST can be improved by increasing the damping of the prototype structure. When the time step of the CR algorithm is less than 0.01 s, the stability regions drawn by the two kind of methods are almost the same. Meanwhile, the continuous method can be directly used for the stability analysis as it is. However, when the integration time step is greater than 0.01 s, the stable region obtained by these two methods show some differences due to the integration algorithm considered. And the influence introduced by the numerical integration algorithm must be considered. At this time, it is recommended to adopt the discrete analysis method proposed for stability analysis, combined with time delay to consider the influence of the actual integration algorithm.