A method for reprofiling at least one rail of a laid rail track formed by the rails, at least in the section of its running surface located at the rail head, comprising the following steps: - providing a machining vehicle, wherein the machining vehicle is movable along the rail track, - providing a machining unit, wherein the machining unit is arranged on the machining vehicle and the machining of the running surface to be machined is carried out during the travel of the machining vehicle, the machining unit comprising - at least a first machining aggregate with at least one rotationally driven chip-removing machining tool, wherein the at least one machining tool is formed as a milling wheel with a plurality of cutter head cutting edges arranged circumferentially one behind the other and aligned along the rail head profile to be reprofiled, - at least one second machining aggregate, - machining the rail head in the section of its running surface in a first machining step by means of the at least one chip-removing machining tool, wherein in the first machining step the material removal is carried out in a milling process, and a surface corrugation with corrugation crests and corrugation troughs is formed during this material removal in the direction of the longitudinal extension of the rail, and the surface corrugation is reduced and/or modified in a subsequent second machining step by means of the second machining aggregate, - wherein during the reduction of the surface corrugation in the second machining step, at least the corrugation crests are plastically deformed and leveled, and - wherein the plastic deformation of at least the corrugation crests is performed by means of at least one forming force directed towards the running surface to be machined, characterized in that - the at least one forming force is applied in a pulsating manner and the material of the rail is displaced slightly in the process and that in the second machining step, no continuous support of a machining tool of the second machining aggregate on the running surface to be machined is performed. - providing a machining vehicle, wherein the machining vehicle is movable along the rail track, - providing a machining unit, wherein the machining unit is arranged on the machining vehicle and the machining of the running surface to be machined is carried out during the travel of the machining vehicle, the machining unit comprising - at least a first machining aggregate with at least one rotationally driven chip-removing machining tool, wherein the at least one machining tool is formed as a milling wheel with a plurality of cutter head cutting edges arranged circumferentially one behind the other and aligned along the rail head profile to be reprofiled, - at least one second machining aggregate, - at least a first machining aggregate with at least one rotationally driven chip-removing machining tool, wherein the at least one machining tool is formed as a milling wheel with a plurality of cutter head cutting edges arranged circumferentially one behind the other and aligned along the rail head profile to be reprofiled, - at least one second machining aggregate, - machining the rail head in the section of its running surface in a first machining step by means of the at least one chip-removing machining tool, wherein in the first machining step the material removal is carried out in a milling process, and a surface corrugation with corrugation crests and corrugation troughs is formed during this material removal in the direction of the longitudinal extension of the rail, and the surface corrugation is reduced and/or modified in a subsequent second machining step by means of the second machining aggregate, - wherein during the reduction of the surface corrugation in the second machining step, at least the corrugation crests are plastically deformed and leveled, and - wherein during the reduction of the surface corrugation in the second machining step, at least the corrugation crests are plastically deformed and leveled, and - wherein the plastic deformation of at least the corrugation crests is performed by means of at least one forming force directed towards the running surface to be machined, characterized in that - the at least one forming force is applied in a pulsating manner and the material of the rail is displaced slightly in the process and that in the second machining step, no continuous support of a machining tool of the second machining aggregate on the running surface to be machined is performed.