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The design of code-division multiple-access (CDMA) transmission systems for satellite communications requires an appropriate consideration of the distortion effects due to on-board nonlinear amplification. The aim of this paper is to provide an analytical framework for the evaluation of the in-band nonlinear distortion effects on the performance of CDMA systems. Both synchronous systems with orthogonal codes and asynchronous systems are considered. It is first shown that, when the users accessing the channel have the same power and their number is sufficiently large, the nonlinear distortion in the decision variables at the receiver can be simply described by a complex scale factor, which depends on the high-power-amplifier (HPA) characteristics only, and an additive noise, which is uncorrelated to the useful signal. Moreover, an analytical formulation of the bit error probability and the total degradation as a function of the output back-off and number of users is given. In the results, which are obtained for three classes of HPA models (i.e., the traveling wave tube amplifier, the solid-state power amplifier, and the amplifier with ideal predistortion), the performance and the capacity of power-limited systems is also discussed.