TOPEX/POSEIDON altimeter data referenced to geoid JGM2 are assimilated into an eddy-resolving quasi-geostrophic ocean model. The location of the model domain is the African sector of the Antarctic Circumpolar Current. All lateral boundaries of the model domain are open. The model has three layers, a spatial resolution of approximately 20 km and realistic bottom topography. The adjoint method (4DVAR) is used to optimize control variables which are the initial state of the stream function and the time dependent boundary values of the stream function and the relative vorticity. Both the numerical implementation of the model and the assimilation method are formulated such that the model can be placed in any ocean location without difficulties. A two-step procedure is applied where first the initial values are optimized. In the second step the time dependent boundary values are adjusted for assimilation periods which are several times longer than the decorrelation times of the initial field. A number of experiments are reported with assimilation periods of different length up to 60 days. For short assimilation periods the error can be reduced from a first guess error of 34 cm root mean square to 5 cm. However, our results indicate that in a long time limit the lowest achievable error lies between 10 and 12 cm. This seems to be due to the model's inability to represent the dynamics of the data sufficiently well. ¿ 1999 American Geophysical Union