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Apnea is defined as an absence of respiratory effort of 20 seconds for larger infants and five seconds for smaller infants. Due to its effect on brain cells, apnea is considered as a life threatening event. In this dissertation, neural networks were used as a tool to recognize apnea, and to determine the length and frequency of apnea. The networks, Madaline, BackPropagation (BP), and Adaptive Bidirectional Associative Memory (ABAM), were chosen based on the advantages of layered networks. Respiratory efforts of infants who had apneic episodes were used to train the networks. Two sensors, transthoracic electrical impedance sensor and strain gauge compliant sensor, were used to record respiratory efforts. The data were presented to the networks in two ways; direct and histogram representations. A pilot study was performed to select proper neural network structure for apnea recognition. The BP trained with the data which was introduced by histogram representation was found to be a proper neural network due to the high recognition accuracy obtained in training and testing stages. Then, several designed experiments were conducted to find a combination of parameters to optimize the BP. In these experiments, the number of hidden neurons, the learning rate, and the momentum term were considered as major factors which affect the overall performance. The results showed that the BP trained with eight hidden neurons, a learning rate of 0.85, and a momentum term of 0.9 was able to provide a recognition accuracy of 96.8% in training.After determining the optimum parameters for the BP, the network was retrained with a total set of 460 training patterns consisted of a wide variety of respiratory efforts, and obtained a recognition accuracy of 99.8% in training. A sequential testing procedure was employed to provide useful information based on the length of apnea and the frequency of apnea. Recognition accuracies of 96.7% for the electrical impedance, and 93.6% for the strain gauge patterns were obtained.