Abstract : A new method for estimating nonlinear instantaneous channels in a multiuser Code Division Multiple Access (CDMA) environment is presented in this paper. This kind of nonlinear models has important applications in the field of telecommunications, e.g. to model uplink channels in Radio Over Fiber multiuser communication systems. The proposed technique is based on the decomposition of a tensor composed of covariances of the chip-rate sampled received signals, the transmitted signals being assumed to be Phase Shift Keying (PSK) modulated. The considered tensor-based approach allows a great flexibility on the number of antennas and the spreading factor, which is particularly desirable when identifying nonlinear systems. Two blind channel estimation algorithms are considered: the Alternating Least Squares (ALS) algorithm and a non-iterative algorithm based on Eigenvalue Decompositions (EVD). The performance of the proposed estimation algorithms is illustrated by means of computer simulations.