In this paper, a neuro-contouring control scheme for the high precision machining of CNC machine tools is descrihed. The proposed control system consists of a conventional controller for each axis and an additional neuro-controller. For contouring control, the contour error must be computed during realtime motion, but generally the contour error for nonlinear contours is difficult to he directly computed. We, therefore, propose a new contour error model to approximate real error more exactly, and here we also introduce a cost function for better contouring performance and derive a learning law to adjust the weights of the neuro-controller. The derived learning law guarantees good contouring performance. Usefulness of the proposed control scheme is demonstrated hy computer simulations.