The paper proposes several mathematical models of the multidirectional associative memory (MAM) neural network by analyzing its structure. A model of MAM with distributed delays is studied. Under some new assumptions on activation functions, 2 n 0 [m/2] invariant subsets of MAM are constructed. Then the existence and the exponential stability of 2 n 0 [m/2] periodic solutions located on invariant subsets are obtained by constructing a suitable Liapunov function and a Poincaré mapping. An estimating method of the exponential convergence rate is given. The obtained results are new to MAM neural networks. An example is given to illustrate the effectiveness of the results.

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