The responses of two types of soft basins for incident SH, SV, P, and Rayleigh waves in a 2-D elastic half-space are investigated with special reference to the long duration of strong motions observed in Mexico City during the Michoacan, Mexico, earthquake of 1985. First, the difficulty for simple 1-D models to reproduce the later part of the accelerogram observed in Mexico City is shown. Then the effect of a 2-D deep basin structure of a relatively large scale (10 km wide and 1 km deep) and a moderate impedance ratio (2.5) is studied. The results show that surface waves generated at the edges of the basin are clearly propagating inside the basin back and forth. However, the increase in duration by these surface waves is 20 sec at most. Introducing another much softer layer inside the basin, we found that the calculated durations and envelop shapes become very similar to the observed ones because of the slowness of surface-wave propagation. These theoretical studies suggest that the exceptionally long duration observed in Mexico City might be caused by a strong, constructive interaction of soft-surface layers with a deep basin structure beneath the city.