Aceelerograms recorded on the Guerrero, Mexico, strong motion accelerograph network illustrate the dependence of strong ground motion on the magnitude and the hypocenter distance. These data suppport the hipothesis that complexity in accelerograms at short distances arises from complexity at the source. The duration of strong shaking is controlled by the source dimension at short distances, and extended by wave porpagation effects as distance increases. Peak amplitudes (peak acceleration, velocity) saturate at different magnitudes at different distances. This change in shape of attenuation curves as magnitude increases can be explained by the trnasition of Green's functions from simple, short pulses at short distances to longer duration wave trains at large distances. Spectral amplitudes demonstrate scalin relations in which loe frequency amplitudes are proportional to seismic moment but high frecuencies increase much less rapidly. The beginnings of large earthquakes look like small earthquakes, consistent with a cascade model for the growth of large events. The mostrecent large earthquake, on sept. 14,995 (Mw=7.4) shows surprisingly weak peak accelerations.