Abstract: In order to machine a multidimensionally curved surface on a workpiece using an electro-erosion, i.e. spark erosion or electro-chemical erosion, machine tool, the machine tool is provided with a tool electrode which has an effective machining face inclined to the direction in which the advance feed drive of the machine tool advances the tool electrode towards the workpiece. By using transverse feeding mechanisms for the tool electrode or the workpiece acting under the control of a computer, or by using a cam and guide arrangement coupled to the tool electrode, the tool electrode and workpiece are so relatively moved that the effective machining face of the electrode always moves in the direction of the momentary largest radius curvature of the curve to be machined. When a cam and guide arrangement is used, the tool electrode can be coupled to the advance feed drive by way of a coupling device which incorporates a universal joint, or a domed surface sliding joint.