Abstract: In this paper, the aftershocks sequences of large earthquakes, M≥7, occurred in South-west and North China indicate alternatively high and low seismic activity on the M-log t diagrams, giving rise to the notion of pseudo-periodicity. By fitting the times of occurrence, t_n, of the strongest aftershock of each interval of high seismic activity of an aftershock sequence with the peak values of the periodic function S(t)=sin(2πt)/T(t)+(π/2) of period T(t), we found that the linear relation log T=loga+qlogt holds, which means T(t)=at^q. It is proposed that the increase of T with t according to a power function is mainly due to the fact that the loading rate \dotP decreases with time in accordance to a power function.By exatrapolation we cam predict the time of occurrence of the next strong aftershock by the next peak value of S(t). The relation between the time interval of two neighbouring strong aftershocks and their magnitudes has also been discussed.