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In this paper, two types of spectrally overlaid multiple symbol-rate (MSR) asynchronous space-time block coded (STBC) multicarrier code division multiple access (MC-CDMA) systems are proposed. One of the systems has constant spreading gain (CSG) and the other has variable spreading gain (VSG) for different services. Both systems have different symbol rates at each subcarrier for different services. Two possible configurations of CSG systems are also proposed. A transmit power control is proposed to maintain the link quality and improve the system capacity. The multiple access interferences and hence system capacities for the two types of MSR STBC MC-CDMA systems are investigated. From the numerical results obtained, it can be concluded that both the MSR STBC MC-CDMA systems with VSG and with CSG configuration 2 can obtain much steadier performance and system capacity than the system with CSG configuration 1. And the system capacity of MSR system with CSG configuration 2 is the best when the number of low rate user is moderate.