We investigate the character of strong ground motion in normal-faulting earthquakes from the western USA, Italy, Greece, Turkey and New Zealand, with magnitudes from 4 to 7.5.In all cases where seismic phases can be identified, peak horizontal ground acceleration occurs in the direct S-phase. Crustal anelasticity for S-waves, which varies locally, is shown for events above magnitude 5 at distances of tens of km to be relatively unimportant in comparison with geometrical spreading in determining the variation of peak horizontal ground acceleration with source-station distance. This permits us to treat our set of records, regardless of source region, as a single worldwide data set. For events between magnitudes 4 and 5, peak horizontal ground acceleration appears not to be controlled by geometrical spreading. At source-station distances greater than about 10 km, it decreases approximately in inverse proportion to distance squared.Earthquakes with magnitudes greater than 5 cause ground acceleration equivalent to that in reverse-faulting and strike-slip events. This result contradicts the widely held view that normal-faulting earthquakes generate systematically smaller ground accelerations than other events. It implies that the orientation of the crustal stress-field, which will be very different in extensional regions from other regions, has little effect on the amplitude of high-frequency seismic waves generated by earthquakes.