The most recent great earthquakes that occurred along the Nankai trough are the 1944 Tonankai and 1946 Nankaido earthquakes. The aftershock areas of both events are smaller than the tsunami source areas, and the seismic moments estimated from geodetic or tsunami data are much larger than those estimated from seismic data. Until now these discrepancies have not been reconciled. We propose a model based on analysis of tsunami waveform data. We find that the rise time is very short on the portion of the fault plane corresponding to the aftershock area, while rupture lasts for 3--9 min. on the rest of the fault where aftershocks were absent. Since the easternmost portion of the 1944 fault slipped slowly and acted as a relaxation barrier, the 1944 rupture might have stopped here. The seismic moments of the 1944 and 1946 events on the basis of both tsunami and geodetic data are 2.8¿1021 Nm and 4.0¿1021 Nm, respectively; the moments of the portions with short rise time are consistent with the previous seismic estimates by Kanamori [1972>.¿ 1997 American Geophysical Union