The Guerrero, Mexico, accelerograph network has recorded, at short distances, earthquakes with magnitudes from 3.0 to 8.1. In this article, the initial 3.5 sec of the P waves, on the vertical component, are compared. In addition to unfiltered accelerograms, several causal bandpass filters are applied. We do not see significant differences, in either original or filtered records, between the initial (e.g., 0.5 sec) seismograms of moderate and large earthquakes. In the original and 2- to 5-Hz passband, the main differences among events with magnitudes over about 4.5 is in the duration of shaking. The initial ground motions of all the large events have very small amplitudes, which gradually get larger. At lower frequencies, seismograms of the largest events show a complex series of multiple pulses, assumed related to failure of numerous asperities. In our lowest frequency band (0.2 to 0.5 Hz), most of the large events that we examined begin with rupture of asperities that are not necessarily larger, and are sometimes smaller, than the asperities that fail during smaller events. The observations are consistent with a model of faulting in which the largest asperities are located at random on the eventual fault plane, and fail when the rupture front, propagating from the hypocenter, reaches them. This allows the largest asperities to occasionally be at the hypocenter and to fail immediately, but for a large fault, it is more likely that they will be located elsewhere and fail later.