Real-time hybrid testing is an attractive method to evaluate the response of structures under earthquake loads. The method is a variation of the pseudodynamic testing technique in which the experiment is executed in real time, thus allowing investigation of structural systems with time-dependent components. Real-time hybrid testing is challenging because it requires performance of all calculations, application of displacements, and acquisition of measured forces, within a very small increment of time. Furthermore, unless appropriate compensation for time delays and actuator time lag is implemented, stability problems are likely to occur during the experiment. This paper presents an approach for real-time hybrid testing in which time delay/lag compensation is implemented using model-based response prediction. The efficacy of the proposed strategy is verified by conducting substructure real-time hybrid testing of a steel frame under earthquake loads. For the initial set of experiments, a specimen with linear-elastic behavior is used. Experimental results agree well with the analytical solution and show that the proposed approach and testing system are capable of achieving a time-scale expansion factor of one (i.e., real time). Additionally, the proposed method allows accurate testing of structures with larger frequencies than when using conventional time delay compensation methods, thus extending the capabilities of the real-time hybrid testing technique. The method is then used to test a structure with a rate-dependent energy dissipation device, a magnetorheological damper. Results show good agreement with the predicted responses, demonstrating the effectiveness of the method to test rate-dependent components.