Over 3 years of TOPEX altimeter data have been used to estimate annual heat storage and long-period heat storage rates in 1¿ grids over the global oceans (65 ¿S to 65 ¿N). The mean annual heat storage rates computed from the TOPEX data agree with those computed from monthly-mean temperatures to within 30 W m-2. The accuracy of long-term heat storage rates is estimated to be less than 10 W m-2 over mid and low latitudes. Regional heat storage rates are larger than this error in many regions, most notably in the tropical Pacific and Indian Oceans and in the northern Atlantic Ocean. The heat storage changes associated with the 1991--1993 El Ni¿o event are evident and agree with values computed from in situ measurements collected by the Tropical Ocean-Global Atmosphere program Tropical Atmosphere Ocean array moorings. The heat storage rates inferred from TOPEX data are also shown to qualitatively agree with sea surface temperature rates computed over the same time period. Finally, heat storage rates are integrated over ocean gyres to estimate atmosphere-ocean heat fluxes. Results suggest that from 1993 to 1995 the North Atlantic and the southern hemisphere gained heat from the atmosphere at a rate of between 1.5 and 2 W m-2, while the North Pacific either lost heat or maintained zero net flux. However, the estimated error on this measurement is of the order of 1.5 W m-2 indicating the true flux could be from 0 to 3 W m-2. Both the TOPEX and temperature measurements suggest that the North Atlantic gained more heat per unit area than the North Pacific between 1992 and 1995.¿ 1997 American Geophysical Union