Multiword expressions (MWEs) are lexical items that can be decomposed into multiple component words, but have properties that are unpredictable with respect to their component words. In this paper we propose the first deep learning models for token-level identification of MWEs. Specifically, we consider a layered feedforward network, a recurrent neural network, and convolutional neural networks. In experimental results we show that convolutional neural networks are able to outperform the previous state-of-the-art for MWE identification, with a convolutional neural network with three hidden layers giving the best performance.