In industrial precision applications using dual-axis micro-positioning stages powered by piezoelectric actuators (PEA), the trajectory tracking and contour following performances are limited due to PEA's inherent hysteretic nonlinearity and time varying parameters. In order to cope with this problem, a position control scheme based on reinforcement learning cerebellar model articulation controller (RLCMAC) is developed in this paper. In the proposed control scheme, for each individual-axis, a CMAC-based feedforward controller with reinforcement learning scheme and a conventional proportional-integral (PI) feedback controller are used. Moreover, in order to reduce contour errors, a CMAC-based cross-coupled controller (CMAC-CCC) is applied to improve the contouring accuracy of a dual-axis micro-positioning stage. Finally, an integrated control scheme is proposed to improve the tracking and contouring accuracy. Experimental results verify the effectiveness of the proposed approach.