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The global monitoring of river discharges is a technologically challenging problem, with important applications in a variety of disciplines. Due to the limited availability and/or quality of river runoff data from many regions, an increasing use of remote sensing techniques is highly desirable. Altimeter specialists have already demonstrated water level retrievals in rivers from available data. The along-track interferometric synthetic aperture radar [along-track InSAR (ATI)] capabilities of state-of-the-art imaging radars on satellites such as the German TerraSAR-X, which was launched on June 15, 2007, also permit high-resolution line-of-sight surface current measurements. In this paper, we evaluate the potential of current measurements in rivers by spaceborne ATI on the basis of fundamental theoretical considerations, existing spaceborne InSAR data from the shuttle radar topography mission (SRTM), and simulated TerraSAR-X data. We show that an SRTM-derived line-of-sight surface current field in the Elbe river, Germany, agrees well with numerical hydrodynamic model results. The data quality is sufficient to resolve characteristic lateral variations of the currents in the river around a pronounced main flow channel. Assuming that the flow direction is usually aligned with the river bed, even a quasi-2D total surface current field can be derived. Simulations indicate that TerraSAR-X was even better suited for current measurements in rivers. Depending on width, surface roughness, and relative flow direction of a river, current estimates with an accuracy better than 0.1 m/s were possible with an effective spatial resolution of a few hundred meters to kilometers.