This paper develops a new technique to estimate an aseismic reliability function of building structural systems with strong nonlinearity considering a low cycle fatigue as a strength deterioration in the hysteretic characteristics. Numerical caculation was carried out to investigate the effect of strength deterioration of hysteretic characteristics on the safety of each story. The results show that the strength deterioration, caused by accumulation of mean plastic flow response, has a tendency to concentrate in a certain definite story, to which the lower safety probability is given.