The magnitude-frequency relation and the constant stress drop are fundamental features of earthquakes, to which a full physical explanation has yet to be given. We present a model that can reproduce the above two fundamental features simultaneously and spontaneously. The model is two-dimensionally configured spring-loaded blocks with a velocity-weakening friction law. We change widely the dynamic friction parameter, which results in the frequency distributions showing the critical, subcritical and supercritical behaviors. Seismicity near the critical state is characterized by almost constant stress drops and the b-value of 1, in which a self-healing pulse maintains its frontal dynamic stress at a level near the static friction in an environmental stress heterogeneity that has evolved through the healing process itself. ¿ 1999 American Geophysical Union