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Recently, two non-adaptive algorithms have been proposed for blind channel estimation for multicarrier CDMA. The first one was proposed by Tureli et al. and the second one by Escudero et al. We develop in this paper two adaptive versions for the first algorithm that are based on the gradient. Whereas, for the second one, we propose an adaptive version that is based on a low-cost subspace adaptive algorithm (NOOJA). In both cases, our adaptive versions perform well while offering at the same time a low computational complexity as compared to their original non-adaptive versions.