Predictions of ground motion for Mexico City during future large earthquakes are currently based on statistical analysis of the large quantity of data recorded by the Mexico City Accelerograph Network (MCAN). In spite of the robustness of these predictions, large uncertanties come from our lack of a physical model that is able to account for the observations. In this article we present such a model based on analysis of strong-motion records obtained during the 25 April 1989, Guerrero earthquake and on numerical modeling. Data analysis suggests that the large amplitudes and very long duration of ground motion observed in the lake-bed zone in Mexico City result from the interaction of diffracted wave trains of Rayleigh waves and the very soft, clay layer that covers the ancient lake of Mexico City. Numerical modeling supports this hypothesis and indicates that this interaction is possible in spite of the largely different scales (kilometers for the incident surface waves, and tens of meters for the clay layer). Lateral heterogeneities split incoming wave trains into different modes. Each is strongly amplified, and its duration is increased by the soft clay layer at its resonant frequency, resulting in the very long monochromatic ground motion that has been the subject of a large number of articles since the 1985 Michoacan earthquake.