The cerebellar model articulation controller (CMAC) neural network is a practical tool for improving existing nonlinear control systems. A typical simulation study is used to clearly demonstrate that the CMAC can effectively reduce tracking error, but can also destabilize a control system which is otherwise stable. Then quantitative studies are presented to search for the cause of instability in the CMAC control system. Based on these studies, methods are discussed to improve system stability. Experimental results on controlling a real world system are provided to support the findings in simulations.