Vertical, teleseismic P waves recorded for the 1979 March 14 Petatlan, Mexico, earthquake were used to derive the distribution of coseismic slip using a linear finite-fault inversion scheme that solves for the amount of slip in each of a series of consecutive time windows. Data recorded by six stations of the Global Digital Seismograph Network were inverted in addition to digitized analogue long-period recordings available from nine Worldwide Standardized Seismograph Network stations. The digital data include four broad-band and short-period velocity waveforms reconstructed from the short- and long-period components. The time-window approach allows for a variable rise time on the fault and accounts for the source multiplicity evident in the recorded P waveforms. Synthetic tests conducted using the inversion method on the limited data set, however, reveal that the data are insufficient to identify the exact dislocation duration on the fault. The method is thus implemented by prescribing the fault rise time using five consecutive 1 s time windows. The coseismic slip inferred from the P waves shows a small 70 cm peak near the earthquake hypocentre and a large zone of dislocation (1.2 m maximum) further south-east. The slip pattern covers depths from 3 to 25 km and is located south-east of other recent large interplate ruptures on the Michoacan segment of the Mexican subduction zone. This result indicates that the 1979 Petatlan earthquake broke an independent, adjacent portion of the Cocos-North America plate boundary. The seismic moment of 1.5 × 10²⁷ dyn cm inferred from the P waves is approximately one-half the long-period moment estimated by other investigators from the observed surface waves. Although the discrepancy is within the uncertainty of the seismic-moment estimates, it may suggest the presence of a component of slow interplate motion that did not radiate significant P-wave energy.