A computer-actuator on-line test of the braced frame with the hysteretic damping device proposed in the author's previous papers, which needs no assumptions for the restoring forces of structures and so that is one of the most promising approaches to trace the elasto-plastic behaviors and especially fracture process of structures, is presented. Outline of the present test system is summarized, in which new, effective error correction procedures are employed in order to eliminate the difference between computed and actually measured displacements, often called as the "displacement control-error", and its accuracies are verified by simple Single-Degree-Of-Freedom (S.D.O.F.) elastic response tests. Based on these verification tests, a series of S.D.O.F. elasto-plastic response tests to the earthquake ground motions are performed. Also, after the restoring force characteristic of the hysteretic damping device in the test being idealized to two numerical models, which are of the bi-linear and the Ramberg-Osgood's type respectively, the accuracies and the validities of these models in -the earthquake response analyses are clarified by comparing with the experimental results.