The affine projection algorithm (APA) represents a popular choice in system identification scenarios, especially with correlated input signals. In this paper, we address the multilinear identification problem, in the framework of multiple-input single-output systems. The main challenge consists of a large parameter space, which can be efficiently reshaped into a tensorial form. The proposed tensor-based APA is tailored for the identification of such multilinear forms, since it combines the solutions provided by the individual (shorter) filters. Simulation results indicate the appealing performance of this algorithm.