Abstract
Non-linear dynamical steady state responses and their compatible condition of one and two story buildings with the hysteresis properties, whose each story is in state of plasticity were given by approximate procedure, which is attributed to solving the boundary value problems in Galerkin's method, provided that non-linear systems with hysteresis properties can be replaced by linear systems with an equivalent viscous damping. From the results evaluated in such manner as mentioned above, consideration as to the optimum seismic coefficient was presented.