We study the space-time relationships between strong earthquakes in California and the intermediate-magnitude earthquakes that both precede and follow them. All 11 earthquakes in California with nominal magnitudes greater than or equal to 6.8 from 1941 to 1993 were preceded by an increase in the rate of occurrence of earthquakes having magnitudes greater than 5.1. Ten of the 11 earthquakes occurred when or shortly after the intermediate magnitude activity was greater than its 75th percentile. Three of these strong earthquakes are in a conventional space-time foreshock-aftershock relationship with others of the 11 strong events. The precursory activity is concentrated in regions having linear dimensions of the order of a few hundred kilometers; these dimensions are significantly larger than the estimated fracture lengths of the ensuing strong earthquakes. The correlations are ill defined for smaller earthquakes and are almost unidentifiable for earthquakes with magnitudes less than about 4.6. The precursors to the strong earthquakes appear over a time interval of the order of 5 to 10 years before the strong earthquake, although the onset was about 25 years before the San Francisco earthquake. In the case of the Loma Prieta and San Francisco earthquakes, the onset of increased activity appears to be relatively abrupt. The increased activity is either switched off abruptly to distances of the order of hundreds of kilometers shortly after the occurrence of a strong earthquake, or the strong events are themselves part of a precursory pattern of continuing high activity before a second strong earthquake that takes place soon thereafter, with subsequent extinction of activity after it. Thus the intermediate-magnitude precursors do not directly influence the time and location of the subsequent strong event, but the strong event has a strong influence on the stress field in the vicinity of intermediate-magnitude earthquakes to distances of the order of many times the scale size of the strong earthquake. ¿ American Geophysical Union 1996