Geosat sea surface height data are assimilated into an eddy-resolving quasi-geostrophic open ocean model using the adjoint technique. The method adjusts the initial conditions for all layers and is successful on the timescale of a few weeks. Time-varying values for the open boundaries are prescribed by a much larger quasi-geostrophic model of the Antarctic Circumpolar Current (ACC). Both models have the same resolution of approximately 20¿20 km (1/3¿¿1/6¿), have three layers, and include realistic bottom topography and coastlines. The open model box is embedded in the African sector of the ACC. For continuous assimilation of satellite data into the larger model the nudging technique is applied. These results are used for the adjoint optimization procedure as boundary conditions and as a first guess for the initial condition. For the open model box the difference between model and satellite sea surface height that remains after the nudging experiment amounts to a 19-cm root-mean-square error (rmse). By assimilation into the regional model this value can be reduced to a 6-cm rmse for an assimilation period of 20 days. Several experiments which attempt to improve the convergence of the iterative optimization method are reported. Scaling and regularization by smoothing have to be applied carefully. Especially during the first 10 iterations, the convergence can be improved considerably by low-pass filtering of the cost function gradient. The result of a perturbation experiment shows that for longer assimilation periods the influence of the boundary values becomes dominant and they should be determined inversely by data assimilation into the open ocean model. ¿ American Geophysical Union 1995