Abstract: The newest method to study earthquake clustering at critical point, namely the time-fram e coefficient method is introduced in this paper, and the characteristics of earthquake clustering of different types and their causes are discussed. On the basis of study on the large earthquakesequence with M≥ 8. 0 in China's mainl and and the sequence with M≥ 6. 0 in North China, the features of self-similarity and timediversity phenomenon in critical state are consequently proposed. In addition, internal time of earthquake generation system isdefined and the nonlinear characteristics of earthquake clustering are studied. The followingresults are obtained: ① An event occurrence means alarge quantity of energy release and state conversionone time. Only when the behavior of earthquake generation system is of enough r and omness, the state conversion and the events may occur. ② Fluctuation is thedetector of earthquake gen-eration system. When the system is in the critical state, the magnitude of fluctuation gets greater and time-framecoefficient equals 1. The clustering in the critical state isdetermined by intrinsicr and om feature and thus seismic events occur stochastically. There w on't be onlyone critical point with coefficientW= 1. ③ Seismic events (M≥ M₀) occurred sequentially reflect the process and its feature of earthquake generation system; Clusteringreflects theordering and disordering feature of the system. ④ Ev ent clustering and clustered events are of the fea-ture of self-similarity and fractal form and also of the feature of self-organization and mapping. ⑤ Time-fram e coefficient, internal time (or age) of the earthquakesystem, the linear equation of interval and past time, mapping and the method of repeating calculation can be used to pre-dict the trend of earthquakes and critical points in the future for the selected earthquakese-quence with M≥ M₀.

Key words: Earthquake clustering, Non-linearity, Self-similarity, Timediversity phe-nomenon, Critical state