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In this paper, an adaptive neural network control strategy is presented for motion/force control of a class of constrained mobile manipulators with unknown dynamics. The system is subject to both holonomic and nonholonomic constraints. The control law is developed based on a simplified dynamic model. The adaptive neural network controller is proposed to deal with the unmodelled dynamics in the system and eliminate the need for the error prone process in obtaining the LIP form of the system dynamics. In addition, the time-consuming offline training process for the neural network is avoided. Proportional plus integral feedback control is used for force control for the benefit of real-time implementation. The proposed control strategy guarantees that the system motion asymptotically converges to the desired manifold while the constraint force remains bounded.