Abstract: A process and device for machining a workpiece supported within a workpiece holder and having a tool which has a machining zone for machining the workpiece and supported within a tool holder. The workpiece and the tool are moved relative to one another in a machining movement for removing workpiece material to form a curved surface on the workpiece, and only a portion of the machining zone of the tool acts upon the workpiece in substantially all machining positions and forms an instantaneous machining zone. The tangent of the machining zone of the tool and the tangent of the surface of the workpiece are each oriented substantially at a right angle with respect to the direction of removal of material from the workpiece and substantially coincide within the instantaneous machining zone.