Titel: Flowing maps to minimal surfaces Abstract: We introduce and analyse a new geometric flow that has elements in common with both the harmonic map flow and with the mean curvature flow. Starting from appropriate initial maps between a closed surface and a general Riemannian manifold, the flow deforms the map towards a parametrisation of a (branched ) minimal surface in the target manifold and can thus be used to give a new proof of the classical results of Sacks-Uhlenbeck and Schoen-Yau on the existence of branched minimal immersions.