We applied the wavelet transform in an attempt to detect long-period components early in a seismogram. We analyzed the displacement seismograms of the 26 December 2004 Sumatra-Andaman earthquake (Mw = 9.2) and the 28 March 2005 Nias earthquake (Mw = 8.7). Wavelet analysis is able to clearly distinguish the amplitudes of the long-period W phase between the seismograms of the two earthquakes before the S wave reaches the station. It shows that the 2004 earthquake generates a W phase of significantly greater amplitude. This facility has potential application to the rapid identification of truly great earthquakes with high tsunami potential.