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This paper studies a class of new neural networks referred to as switched neutral-type neural networks (SNTNNs) with time-varying delays, which combines switched systems with a class of neutral-type neural networks. The less conservative robust stability criteria for SNTNNs with time-varying delays are proposed by using a new Lyapunov-Krasovskii functional and a novel series compensation (SC) technique. Based on the new functional, SNTNNs with fast-varying neutral-type delay (the derivative of delay is more than one) is first considered. The benefit brought by employing the SC technique is that some useful negative definite elements can be included in stability criteria, which are generally ignored in the estimation of the upper bound of derivative of Lyapunov-Krasovskii functional in literature. Furthermore, the criteria proposed in this paper are also effective and less conservative in switched recurrent neural networks which can be considered as special cases of SNTNNs. The simulation results based on several numerical examples demonstrate the effectiveness of the proposed criteria.