Response of simple structural models to the peculiar ground motions recorded in the lake-bed area of Mexico City was analyzed in order to explain the performance of typical buildings during the 1985 earthquake. Results for one-degree of freedom systems with different kinds of inelastic behavior show that when hysteresis loops remain stable under several cycles of large inelastic deformations, exceptionally large reductions in the structural response take place. Nevertheless, if the hysteresis loops show some degradation of strength for large displacements, the response increases sharply for the same critical periods. Results for multi-degree of freedom systems show large concentrations of ductility demands at lower stories. Static and dynamic analyses of linear and non-linear models of several typical mid-rise concrete buildings were also performed. The results agreed with reasonable accuracy with the observed behavior and with measurements of the response under low amplitude ambient vibrations.