Temporal changes in the Earth's gravity field have been determined by analyzing satellite laser ranging (SLR) observations of eight geodetic satellites using data spanning an interval of over 20 years. The satellites used in the analysis include Starlette, LAGEOS 1 and 2, Ajisai, Etalon 1 and 2, Stella, and BE-C. Geophysical parameters, related to both secular and long-period variations in the Earth's gravity field, including the geopotential zonal rates (J˙2, J˙3, J˙4, J˙5, and J˙6) and the 18.6-year tide parameter, were estimated. The estimated values for these parameters are J˙2=-2.7¿0.4(10-11/yr); J˙3=-1.3¿0.5(10-11/yr); J˙4=-1.4¿1.0(10-11/yr); J˙5=2.1¿0.6(10-11/yr); J˙6=0.3¿0.7(10-11/yr); C18.6+20=1.56¿0.2 (centimeters) and S18.6+20=-0.1¿0.2 (centimeters). The amplitude and phase for the 18.6-year tide are in general agreement with the effects predicted by the Earth's mantle anelasticity. The solution accuracy was evaluated by considering the effects of errors in various non-estimated dynamical model parameters and by varying the data span and data sets used in the solution. Estimates forJ˙3 from individual LAGEOS 1 and Starlette SLR data sets are in good agreement. The lumped sum values for J˙3 and J˙5 are very different for LAGEOS 1 and Starlette. The zonal rate determination is limited to degree 6 with the current SLR data sets. Analysis of the sensitivity of the solution for the zonal rates to the satellite tracking data span suggests that the temporal extension of the current SLR data sets will enhance the solution of zonal rates beyond degree 6.¿ 1997 American Geophysical Union