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Multistability is an important property of recurrent neural networks. It plays a crucial role in some applications, such as decision making, association memory, etc. This paper studies multistability of a class of neural networks with different time scales under the assumption that the activation functions are unsaturated piecewise linear functions. Using local inhibition to the synaptic weights of the networks, it is shown that the trajectories of the network are bounded. A global attractive set which may contain multi-equilibrium points is obtained. Complete convergence is proved by constructing an energy-like function. Simulations are employed to illustrate the theory.