We present what is to our knowledge the first direct observation of the deformation of the surface of the ocean upon passage of a tsunami wave, on the high seas, far from the influence of shorelines and continental shelves. We use satellite altimetry data from the ERS-1 and TOPEX/POSEIDON programs, complemented by spectrogram techniques and synthetic maregrams to examine the case of seven recent tsunamigenic earthquakes. We make a positive identification of the tsunami wave field in the case of the 1992 Nicaraguan tsunami, which we detect at 15 ¿S, 106 ¿W, five hours after origin time. We model the observed spectrogram by injecting a synthetic of variable amplitude into the signal of a repetitive cycle of the satellite along the same track, concluding that the Nicaraguan tsunami had a zero-to-peak amplitude of 8 cm in that region. In the case of the 1995 Chilean tsunami, a large scatter in the spectral properties of the reference tracks renders the detection tentative. We fail to detect the tsunamis of five other large events, including the 1996 Biak and 1996 Peru earthquakes, primarily on account of unfavorable source directivity in the geometry of existing satellite tracks, and of the strong and incoherent noise produced by large current systems, such as the Kuroshio in the Northwest Pacific. ¿ 1999 American Geophysical Union