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Neural networks are receiving attention as controllers for many industrial applications. Although these networks eliminate the need for mathematical models, they require a lot of training to understand the model of a plant or a process. Issues such as learning speed, stability, and weight convergence remain as areas of research and comparison of many training algorithms. This paper discusses the application of neural networks to control induction machines using direct torque control (DTC). A neural network is used to emulate the state selector of the DTC. The training algorithms used in this paper are the backpropagation, adaptive neuron model, extended Kalman filter, and the parallel recursive prediction error. Computer simulations of the motor and neural-network system using the four approaches are presented and compared. Discussions about the parallel recursive prediction error and the extended Kalman filter algorithms as the most promising training techniques is presented, giving their advantages and disadvantages.