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In this paper, we investigate multistability of two kinds of recurrent neural networks with time-varying delays and activation functions symmetrical about the origin on the phase plane. One kind of activation function is with zero slope at the origin on the phase plane, while the other is with nonzero slope at the origin on the phase plane. We derive sufficient conditions under which these two kinds of n-dimensional recurrent neural networks are guaranteed to have (2m+1)n equilibrium points, with (m+1)n of them being locally exponentially stable. These new conditions improve and extend the existing multistability results for recurrent neural networks. Finally, the validity and performance of the theoretical results are demonstrated through two numerical examples.