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In this paper, two gait transition models of a quadruped are derived based on gait kinematics. The learning and generalization capability of the cerebellar model articulation controller (CMAC) neural network in learning gait transitions is then studied. The two gait transition models are the transition between two general periodic gaits and the transition between a periodic gait and a continuous follow-the-leader (FTL) gait, while maintaining FTL mode during the transition. These models are nonlinear and require either heuristic rules or simultaneous solution of several nonlinear equations. Many transition gaits are then generated by these kinematic gait transition models under various gait conditions and evaluated in terms of stability and smoothness of leg movements. The CMAC neural network is then applied to learn the good transition gaits in four transition conditions: (1) from wave gait to wave gait; (2) from wave gait to FTL gait; (3) from walk to trot; and (4) from trot to transverse gallop. The learning and generalization capability of the trained CMAC neural network is evaluated and found to be satisfactory. This study has demonstrated the potential of applying neural networks to learn walking machine gaits and gait transitions.