The study of nonlinear site response has practical difficulties due to large ambiguities in isolating local response from other competing effects. We chose a sedimentary site LF6 in Los Angeles basin that (1) has the closest reference rock sites available, compared to other stations, allowing an accurate estimation of local amplification, and (2) illustrates clear resonance in the near surface. In our opinion, this case represents the least ambiguity in the identification of possible nonlinearity. The site responses during the Northridge, the 1987 Whittier Narrows events and the Northridge aftershocks are compared. The station shows a fundamental resonance-frequency change between the higher- and lower-amplitude motions in the entire ensemble of 17 events used. The net shear-modulus reduction during the Northridge event is a factor of 1.3 to 1.4 compared to the Whittier Narrows event and is a factor of 1.7 compared to the aftershocks. This result provides guidance of what to expect at other sites in the basin, where the nonlinear response is less easy to characterize.