Call admission control (CAC) is becoming vital for multimedia services in the ability of wireless/mobile networks to guarantee Quality of Service (QoS) partially due to the network's limited capacity. In this paper, we propose an optimal call admission control scheme with bandwidth reallocation algorithm (multi-class-CAC-BRA) for multi-classes of adaptive multimedia services in wireless/mobile networks. The multi-class-CAC-BRA approach optimizes revenue for service providers and satisfies QoS requirements for service users. The proposed approach adopts semi-Markov Decision Process to model both call admission control and bandwidth reallocation algorithm. In other words, whenever decisions are made, decisions are made for both call admission control and bandwidth reallocation. Since the non-adaptive multimedia traffic is a special case of the adaptive multimedia traffic, the non-adaptive optimal CAC scheme is a special case of our optimal multi-class-CAC-BRA scheme. Furthermore, the Interior-point Method in linear programming is used to solve the optimal decision problem. Simulation results reveal that the proposed multi-class-CAC-BRA scheme adapts itself well to adaptive multi-class multimedia traffic, achieves optimal revenue, and satisfies QoS requirements that are the upper bounds of handoff dropping probabilities. Our approach solves the optimal adaptive multimedia CAC problem. We believe that this work has both theoretical and practical significance.