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Next generation wireless systems will be required to support heterogeneous services with different transmission rates that include real time multimedia transmissions, as well as non-real time data transmissions. In order to provide such flexible transmission rates, efficient use of system resources in next generation systems will require control of both data transmission rate and power for mobile terminals. In this paper we formulate the problem of joint transmission rate and power control for the uplink of a single cell CDMA system as a non-cooperative game. We assume that the utility function depends on both transmission rates and powers and show the existence of Nash equilibrium in the non-cooperative joint transmission rate and power control game (NRPG). We include numerical results obtained from simulations that compare the proposed algorithm with a similar one which is also based on game theory and it also updates the transmission rates and powers simultaneously in a single step.