A method of repairing a component, in particular a gas turbine component, which is produced from a base material with an oriented microstructure, comprises the steps of: cleaning the repair site, filling the repair site with a filling material corresponding to the composition of the base material, carrying out a heat treatment in the region of the filled repair site, wherein the filling material has micro- and/or nano-scale particles, during the filling of the repair site measures which prevent the oxidation of the filling material are taken, an the temperatures and holding times of the heat treatment are set appropriately for the composition of the filling material and of the base material of the component in such a way that an epitaxial attachment of the filling material to the surrounding bas material takes place.