A robust Sugeno type adaptive fuzzy neural network (RSAFNN) backstepping control for a two-axis motion control system is proposed in this paper. The adopted two-axis motion control system is composed of two permanent magnet linear synchronous motors (PMLSMs). The single-axis motion dynamics with the introduction of a lumped uncertainty, which includes parameter variations, external disturbances, cross coupled interference between the two PMLSMs and fiction force, is derived first. Then, a backstepping control approach is proposed to compensate the lumped uncertainty occurred in the two-axis motion control system. Moreover, to improve the control performance in the tracking of the reference contours, a RSAFNN backstepping control is proposed where a Sugeno type adaptive fuzzy neural networks (SAFNN) is employed to estimate the lumped uncertainty directly. Furthermore, the proposed control algorithms are implemented in a TMS320C32 DSP-based control computer.