A stochastic model is presented for estimating probabilities of exceeding site ground motions due to temporally dependent earthquake events. The model reflects the hypothesized dependence of the size of large earthquake events on the time of occurrence of the last major earthquake. An empirical attenuation relationship is used to describe the ground motion at a site originating from a well-defined fault system. The application of the model to the Middle America Trench is discussed. The seismic hazard potential in Mexico City is computed in terms of probabilities of exceeding peak ground acceleration levels. The results indicate that consideration of the seismic gap is important for estimating the seismic hazard at a site. It is also observed that site hazard estimates are greatly dependent on the specific attenuation relationship used. The need for other approaches of ground motion estimation is recognized.