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A stochastic conjugate gradient algorithm (SCGA) is proposed for the solving of the nonlinear optimization problem associated with the multiuser constant modulus algorithm (CC-CMA) for DS-CDMA receivers in a multiuser environment. The algorithm is referred to as the stochastic conjugate gradient CC-CMA (SCGCC-CMA). Simulations show that the SCGCC-CMA algorithm preserves the fast convergence rate of the block-shanno cross correlation constant modulus algorithm (BSCC-CMA), can be configured to perform similar to the recursive least squares (RLS) version of the CC-CMA algorithm, and can outperform the conventional CC-CMA for less cost. The proposed algorithms can also be used in DS/CDMA systems to solve the problem of joint blind channel equalization and blind source separation in a single-user and multiuser environment. Alternatively, a window sliding parameter may be adjusted to trade off between performance and computation to match system requirements. We also propose a convergence analysis for the proposed algorithms.