We solve the statistical-dynamical equations of an asperity model to obtain both the time-dependent seismicity and the stationary seismicity with its associated magnitude-frequency relation. The parameters of the model are chosen to reproduce the seismicity of the Oaxaca region on the western coast of Mexico. The observed enhancement of the seismicity in the high magnitude range is well reproduced, and the calculated b-value of about. 7 is also acceptable. The predicted features of the time-dependent seismicity are as follows: there is an enhancement of the small scale seismicity immediately following a characteristic earthquake. This enhancement approximately doubles the rate of occurrence of small events relative to the stationary values. Both intermediate and characteristic earthquakes present a gap with a subsequent enhancement of the seismicity superior to long term averages. There are strong correlations between the characteristic and intermediate seismicities, indicating that the latter have premonitory value.