Neural networks can be considered as a massively parallel distributed processing system with the potential for ever improving performance through dynamical learning. The power of neural networks is in their ability to learn and to store knowledge. Neural networks purport to represent or simulate simplistically the activities of processes that occur in the human brain. The ability to learn is one of the main advantages that make the neural networks so attractive. The fact that it has been successfully applied in the fields of speech analysis, pattern recognition and machine vision gives a constant encouragement to the research activities conducted in the application of neural networks technique to solve engineering problems. One of the less investigated areas is control engineering. In control engineering, neural networks can be used to handle multiple input and output variables of nonlinear function and delayed feedback with high speed. The ability of neural networks to control engineering processes without prior knowledge of the system dynamic very appealing to researchers and engineers in the field. The present work concerns the application of neural network techniques to control a simple ball-beam balancing system. The ball-beam system is an inherent unstable system, in which the ball tends to move to the end of the beam. The task is to control the system so that the ball can be balance at an location of the beam within a short period of time, and the beam be kept at an horizontal position. The state of the art of neural networks and their application in control engineering has been reviewed. The computer simulation of the control system has been performed, using both the conventional Bass-gura (chapter 3) method and the neural network method. In the conventional method the system equations were established using the Lagrangian vanational principle, and Euler method has been used to integrate the equations of movement.