The Andreanof Islands earthquake of May 7, 1986 ( Ms = 7.7), is the largest earthquake to have occurred along the Aleutian Arc in the past 20 yr. Source parameters of the mainshock, three large aftershocks (6.1 < Ms < 6.7), and a foreshock ( Ms = 6.0) are determined by inverting digitally recorded teleseismic waveforms and amplitudes. Long-period P and SH waves are inverted simultaneously to determine the strike, dip, rake, centroid depth, source time-function, and seismic moment of each earthquake. Complexities in the rupture process of the mainshock are modeled using broadband (5 to 0.01 Hz) P -wave displacement waveforms. Modeling the mainshock as a propagating line source, the long-period and broadband waveforms indicate that the locus of largest moment release propagated bilaterally along the arc with a well resolved velocity of 1.5 km/sec. The source mechanism is consistent with faulting on a low angle (23 ± 1°) thrust fault. The fault's strike (260 ± 10°) and the rake of the slip vector on the fault (93 ± 8°) are less well-resolved and trade off with each other. Acceptable centroid depths range between 10 and 25 km. Within this range of depths, the misfit of the synthetic to the observed long-period and broadband waveforms varies by only 6 per cent, while moment estimates vary by as much as 64 per cent. For a centroid depth of 20 km, the estimated seismic moment is 1.1 × 1028 dyne cm, 85 per cent of the moment estimated from surface wave analysis. Ninety per cent of the moment release was generated by three patches on the fault surface, all located within 90 km of the nucleation point. Very little moment, however, was released near the epicenter of the mainshock. The epicentral locations, source mechanisms and depths of the foreshock, and one of the aftershocks modeled by us are consistent with faulting on the same thrust plane as the mainshock. The other two modeled aftershocks are located north of the island arc and have source depths of less than 15 km indicating that they occurred within the overriding plate. The focal mechanisms of these events indicate almost pure strike-slip faulting, but the waveform data do not contain sufficient information to distinguish which of the couples of the double-couple mechanism corresponds to the fault plane. Joint relocations of several of the aftershocks from one of these strike-slip earthquakes suggests that right-lateral strike-slip faulting occurred on a northeasterly trending fault plane.