Magnetic resonance (MR) guided high intensity focused ultrasound (HIFU) and external beam radiotherapy (EBRT) interventions, to which we shall refer to as beam therapies/interventions, are promising techniques for the non-invasive ablation of tumors in abdominal organs. Therapeutic energy delivery in these areas becomes, however, challenging due to the continuous displacement of the organs with respiration. Previous studies have addressed this problem by coupling high-framerate MR-imaging with a tracking technique based on the algorithm proposed by Horn&Schunck (H&S), which was chosen due to its fast convergence rate and highly parallelizable numerical scheme. Such characteristics were shown to be indispensable for the real-time guidance of beam therapies. In its original form, however, the algorithm is sensitive to local gray-level intensity variations not attributed to motion such as those that occur, for example, in the proximity of pulsating arteries. In this study, an improved motion estimation strategy which reduces the impact of such effects is proposed. Displacements are estimated through the minimization of a variation of the H&S functional for which the quadratic data fidelity term was replaced with a term based on the linear L 1 norm, resulting in what we have called an L2 -L1 functional. The proposed method was tested in the liver and kidney of two healthy volunteers under free-breathing conditions, on a data set comprised of 3000 images equally divided between the volunteers. Results have shown that, compared to the existing approaches, our method demonstrates a greater robustness to local gray-level intensity variations introduced by arterial pulsations. Additionally, the computational time required by our implementation make it compatible with the work-flow of real-time MR-guided beam interventions. To the best of our knowledge this study was the first to analyze the behavior of an L1 -based optical flow functional in an applicative context: real-time MR-guidance of beam therapies in moving organs.