We study the statistical property and temporal variation of activity due to ruptures on two noncoplanar interactive faults. Each fault is assumed to consist of cracks and intervening asperities. The ruptures are assumed to occur in the form of catastrophic coalescence of the coplanar cracks on each fault. We apply fracture mechanics to the analysis of the interactions among cracks and to the consideration of fracture condition. Our fault model gives rise to a complex frequency distribution of event sizes even if no externally imposed spatial inhomogeneity is assumed for the distributions of cracks and asperities and a homogeneous statistical distribution is assumed for fracture strengths. For the smaller events the frequency distribution of the event sizes obeys the Gutenberg-Richter magnitude-frequency law. It is also shown that the number of smaller events increases as the contribution of noncoplanar interactions increases. We generally observe the periodic recurrence of events after transient change at the beginning of each sequence of activity. The length of the transient part increases considerably as the contribution of noncoplanar interactions increases. The recurrence period at the steady periodic state also lengthens with increasing contribution of noncoplanar interactions. Hence if the temporal variation of activity is observed in a fixed length of time, then the activity appears to be much more complex when the contribution of noncoplanar interactions is larger. It is also observed that events with smaller recurrence intervals are more abundant when the influence of noncoplanar interactions is large. ¿ American Geophysical Union 1995