A frequency domain inversion technique is employed to image the rupture process of the 19 September 1985 Michoacán, Mexico, earthquake. A linear system is derived from the elastodynamic representation theorem and is solved for the spatial slip-velocity distribution, in the frequency bandwidth 0.0 to 0.32 Hz. The temporal behavior of slip velocity on the fault plane is then recovered by Fourier synthesis. Model complexity is penalized by seeking a solution that propagates with the most nearly constant rupture velocity and that produces the most nearly constant spatial slip distribution. At 0 Hz, the inversion of surface static displacements, as inferred from strong-motion recordings of the Guerrero accelerograph array, gives an estimate of the static offset on the fault plane. Coastal uplift data inferred from the mortality of intertidal organisms (Bodin and Klinger, 1986) is also used to further constrain the spatial slip distribution. A low-frequency image of the rupture process of the earthquake has been obtained using full-space Green's functions. Two areas of large slip amplitude are discernible, one located downdip of the reported hypocenter and the other updip of the projection on the fault plane of station La Unión. Their separation is approximately 100 km. Assuming that full-space Green's functions underestimate static offset values at the surface of a half-space by a factor of 0.5, the inferred seismic moment is 10.6 × 1027 dyne-cm, 90 per cent of which is released in these two areas sustaining the largest slip. The total inferred rupture duration is approximately 56 sec. From the hypocenter, the rupture front proceeds with an average velocity estimated at 2.8 km/sec. There are indications of bilateral propagation both from the hypocentral area and from an area surrounding the projection on the fault plane of the strong-motion station La Unión. An upper bound on rupture duration at the two principal subevents is 8 sec.