It has been known since at least 1898 (ref. 1) that sediments can amplify earthquake ground motion relative to bedrock. For the weak ground motion accompanying small earthquakes, the amplification due to sediments is well understood in terms of linear elasticity (Hooke’s law)(2), but there has been a long-standing debate regarding the amplification associated with the strong ground motion produced by large earthquakes. The view of geotechnical engineers, based largely on laboratory studies, is that Hooke’s law breaks down at larger strains causing a reduced (nonlinear) amplification. Seismologists, on the other hand, have tended to remain sceptical of this nonlinear effect, mainly because the relatively few strong-motion observations seemed to be consistent with linear elasticity, Although some recent earthquake studies have demonstrated nonlinear behaviour under certain circumstances(3,4), the significance of nonlinearity for the type of stiff-soil sites found in the greater Los Angeles region remains unresolved(5). Here we report that ground-motion amplification due to sediments for the main shock of the 1994 Northridge earthquake was up to a factor of two less than the amplification observed for its aftershocks, These observations imply significant nonlinearity in such amplification, and bring into question the use of measurements of weak ground motion to predict the strong ground motion at sedimentary sites.