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A magnetic-levitation (maglev) transportation system including levitation and propulsion control is a subject of considerable scientific interest because of highly nonlinear and unstable behaviors. In this paper, the dynamic model of a maglev transportation system including levitated electromagnets and a propulsive linear induction motor (LIM) based on the concepts of mechanical geometry and motion dynamics is developed first. Then, a model-based sliding-mode control (SMC) strategy is introduced. In order to alleviate chattering phenomena caused by the inappropriate selection of uncertainty bound, a simple bound estimation algorithm is embedded in the SMC strategy to form an adaptive sliding-mode control (ASMC) scheme. However, this estimation algorithm is always a positive value so that tracking errors introduced by any uncertainty will cause the estimated bound increase even to infinity with time. Therefore, it further designs an adaptive fuzzy-neural-network control (AFNNC) scheme by imitating the SMC strategy for the maglev transportation system. In the model-free AFNNC, online learning algorithms are designed to cope with the problem of chattering phenomena caused by the sign action in SMC design, and to ensure the stability of the controlled system without the requirement of auxiliary compensated controllers despite the existence of uncertainties. The outputs of the AFNNC scheme can be directly supplied to the electromagnets and LIM without complicated control transformations for relaxing strict constrains in conventional model-based control methodologies. The effectiveness of the proposed control schemes for the maglev transportation system is verified by numerical simulations, and the superiority of the AFNNC scheme is indicated in comparison with the SMC and ASMC strategies.