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, crosscoupled 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.