Machines for machining workpieces, especially metal sheets, include a machining device, a main drive, and an auxiliary drive that is different therefrom. Both drives serve to generate a relative movement between the machining device and a workpiece, wherein the machining device is movable relative to the workpiece and/or the workpiece is movable relative to the machining device with a main movement by means of the main drive and wherein the machining device is movable relative to the workpiece with an auxiliary movement by means of the auxiliary drive. Machines with high adaptability to different machining tasks are provided. Methods of machining workpieces include corresponding method steps.