Student Number : 8315331 - MSc dissertation - School of Electrical and Information Engineering - Faculty of Engineering and the Built Environment / In this dissertation an efficient algorithm to calculate the differential of the network output with respect to its inputs is derived for axis orthogonal Local Model (LMN) and Radial Basis Function (RBF) Networks. A new recursive Singular Value Decomposition (SVD) adaptation algorithm, which attempts to circumvent many of the problems found in existing recursive adaptation algorithms, is also derived. Code listings and simulations are presented to demonstrate how the algorithms may be used in on-line adaptive neurocontrol systems. Specifically, the control techniques known as series inverse neural control and instantaneous linearization are highlighted. The presented material illustrates how the approach enhances the flexibility of LMN networks making them suitable for use in both direct and indirect adaptive control methods. By incorporating this ability into LMN networks an important characteristic of Multi Layer Perceptron (MLP) networks is obtained whilst retaining the desirable properties of the RBF and LMN approach.