Abstract: In this paper, the durations of the sequence of strong aftershocks of 21 shallow major earthquakes, M6.0, occurred in North and Southwest China during 1966-1980 have been discussed, giving some empirical results as follows:(1) The duration △T of such sequences are not the same and they do not seem to be related to the magnitudes of the main shocks.(2) △T's are related to the overall attenuation coefficient (p) of the aftershock frequency of the entire earthquake sequence. For the sequence with p>1, △T150 days and the sequence of strong aftershocks ends at about an inflection point of the attenuation curve of aftershock frequency.There are inevitably exceptions to the empirical relations thus obtained because of the extremely complicated nature of the problem.