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An adaptive receiver based on hybrid system theory is developed for a multiuser multiple-input multiple-output (MIMO) fading code-division multiple-access (CDMA) system. The basic idea is to treat the transmitted symbols and channel gains as unknown states (discrete and continuous) within a hybrid systems framework. The Bayesian-inference-based state estimation is derived using multiple model theory resulting in an optimal joint sequence estimator, which is shown to be intractable in its computational complexity. A suboptimal receiver (IMM-SIC) is then derived based on the well-known Interacting Multiple Model (IMM) algorithm and successive interference cancellation (SIC) scheme. This paper shows the specific approximations made to the probability densities of the optimal receiver in deriving the IMM-SIC receiver with complexity linear in number of users. This receiver design is well suited for online recursive processing of space-time coded CDMA system, where the decoding stage is incorporated within the multiple model framework.