Concerning the dynamic analysis based on the equivalent linearization of the restoring force characteristics of, some examinations taking the mechanism of the analytical procedure into have been conducted with one-degree-of-freedom system. As the results, the of difference between the solutions by equivalent linear method and ones for both steady and unsteady conditions have been clarified. The of difference also clarified. With these results the limit of validity in the application of the linear solutions to the seismic design of structures has been shown clearly. the process of above consideration some of new knowledge concerning the procedure for non-linear dynamic analysis have been obtained and reported.