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In this paper, we are concerned with a class of Clifford-valued fuzzy cellular neural networks with time-varying delays. Based on the Banach fixed point theorem and inequality technique, we obtain the existence and uniqueness of Besicovitch-like almost periodic solutions and global exponential stability of the fuzzy cellular neural network under consideration. Finally, we give a numerical example to illustrate the effectiveness of our results. Even when the systems we consider degenerate to quaternion-valued, complex-valued and real-valued ones, our results in this paper are completely new.