A double inverse method to convert SAR data to estimates of current shear was developed theoretically. Problems of applying the technique to real SAR data were examined. The first step of the inversion process involved elimination of noise in the (→x, →k) wave spectra deduced from SAR images. The second step, estimation of current shear, required the existence of well defined swell and a favorable single of interaction between swell and ocean current. Application of the method in the Antarctic Circumpolar Current encountered sea conditions that both satisfied and violated these requirements. Where the wave-current geometry was favorable, realistic surface current velocity fields were obtained, suggesting the presence of a substantial mesoscale eddy. Another attempt to apply the method in the Gulf Stream produced wave spectral estimates that showed no clear peak and hence produced no current estimates. ¿ American Geophysical Union 1989