The CMAC is a neural network that imitates the human cerebellum. The CMAC can approximate a wide variety of nonlinear functions by learning, and the learning speed is very fast. However, the CMAC requires a large memory space, because it is based on a table look-up method. Furthermore, a trade-off between the required memory space and the approximation accuracy is required in the choice of the quantization interval. A CMAC that changes quantization intervals adaptively, called a memory-based learning system (MBLS), is designed. The MBLS decreases quantization intervals for areas with larger variation, but it increases those for areas with small variation. This improves the approximation accuracy and reduces the required memory space. Computer simulation results for the modelling and control problems are presented.