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We analyzed strong-motion and broadband recordings of two moderate-magnitude earthquakes that occurred in the Nankai Trough. The first event was the 2004 Mw 6.5 southeast off-Kii peninsula earthquake, an aftershock event inside the Philippine Sea Plate near the Nankai Trough axis. The second event was the 2016 Mw 5.8 southeast off-Mie Prefecture earthquake, an independent event in the rupture area of the 1944 Mw ~ 8 Tonankai earthquake. The centroid depths were 11 and 14 km for the 2004 and 2016 events, respectively. Despite a large difference in the moment magnitude between the two events, the JMA magnitude (Mj) was 6.5 for both the events. We found that the short-period ground motions (e.g., response spectra at periods < 1 s) as well as the much longer-period ground motions (> 20 s) for the 2016 event scaled generally well with the moment magnitude of the event. In contrast, the ground motions from the 2016 event were comparable to those for the larger-moment-magnitude 2004 event at equal distances at periods of about 2-20 s in wide areas and the observed acceleration response spectra at those periods were noticeably underestimated for the 2016 event by the ground motion prediction equation (GMPE) that employs Mw. An examination of the existing subsurface velocity model suggested that the difference in the relative location of the two events with respect to the thick accretionary prism of low seismic velocity most probably caused the comparable amplitude of the seismic waves at those periods. As a result, we posit that the values of Mj are equal for the two events because Mj is estimated using the displacement amplitude of ground motions at periods smaller than about 6 s. On the other hand, GMPE employing Mj generally described the observed data well. The results suggested that the plate boundary earthquakes in the Nankai Trough may excite strong long-period ground motions of engineering importance, and these ground motions appear to be better explained by Mj than by Mw in GMPEs for moderate-magnitude earthquakes in the Nankai Trough subduction zone. [ABSTRACT FROM AUTHOR]