Observations of three-dimensional ground motion at a single point on the surface of the Earth following an earthquake can be sufficient to determine the zeroth order moment tensor of the event. We adapt the centroid-moment tensor (CMT) method [Dziewonski et al., 1981> of analysis to single station data and apply it to the September 19, 1985 Michoacan earthquake. The obtained mechanism indicates faulting on a shallow plane, consistent with the ongoing subduction of the Cocos plate. The scalar moment is 1.3¿1028 dyne -cm. A direct deconvolution of the observed P-wave train indicates that the moment release occurred in two subevents, each of 20 seconds duration with a peak-to-peak separation in time of 25 seconds.