We examine the feasibility of using satellite altimeter data to measure the long-term change of global sea level (estimated from tide gauge data to be a rise of approximately 0.2 cm yr-1). Two and one-half years of collinear Geosat altimeter data (1986--1989) are used together with a 17-day set of Seasat altimetry (July--August 1978) having nearly the same ground track. A consistent set of precise orbits was used throughout, and residual orbit error was removed as a sinusoidal fit to approximately 3-day arcs of sea level collinear differences. The globally averaged data show sea level falling at 1.2¿0.3 cm yr-1 Geosat over the first 2 years, even after removal of tide errors and instrument biases not accounted for in the Geosat geophysical data records. This unrealistic result is found to be due largely to long-term error in the ionospheric model for the single-frequency Geosat altimeter. The Geosat-Seasat comparison, based on data 10 years apart, shows an apparent sea level rise of 1.0 cm yr-1. Assuming this result is also unrealistic, a possible explanation is a biased scale to the Doppler-determined Geosat orbit which, unlike Seasat, did not have the benefit of laser tracking. It is also possible that the Geosat altimeter (without external in-orbit calibration) had a bias of the order of 10 cm. We conclude that for satellite altimetry to make a fundamental contribution to monitoring global mean sea level change, both the altimeter (including its media corrections) and the orbit model which provides a geocentric reference for the ocean surface will need continuing and careful calibration with absolute standards. ¿ American Geophysical Union 1992