A robust recurrent-neural-network (RRNN) sliding-mode control is proposed for a biaxial motion mechanism to allow reference contour tracking. The biaxial motion mechanism is a X-Y table of a computer numerical control machine that is driven by two field-oriented control permanent-magnet synchronous motors. The single-axis motion dynamics are derived in terms of a lumped uncertainty that includes cross-coupled interference between the two-axes. A RRNN sliding-mode control system is proposed based on the derived motion dynamics to approximate the control obtained by using sliding-mode control and the motions at the X-axis and Y-axis are controlled separately. The motion tracking performance is significantly improved using the proposed control technique and robustness to parameter variations, external disturbances, cross-coupled interference and frictional torque can be obtained as well. Experimental results on circular, four-leaf, window and star reference contours are provided to show that the dynamic behaviour of the proposed control system is robust with regard to uncertainties.