In this paper, we introduce a novel type of Rectified Linear Unit (ReLU), called a Dual Rectified Linear Unit (DReLU). A DReLU, which comes with an unbounded positive and negative image, can be used as a drop-in replacement for a tanh activation function in the recurrent step of Quasi-Recurrent Neural Networks (QRNNs) (Bradbury et al. (2017)). Similar to ReLUs, DReLUs are less prone to the vanishing gradient problem, they are noise robust, and they induce sparse activations. We independently reproduce the QRNN experiments of Bradbury et al. (2017) and compare our DReLU-based QRNNs with the original tanh-based QRNNs and Long Short-Term Memory networks (LSTMs) on sentiment classification and word-level language modeling. Additionally, we evaluate on character-level language modeling, showing that we are able to stack up to eight QRNN layers with DReLUs, thus making it possible to improve the current state-of-the-art in character-level language modeling over shallow architectures based on LSTMs.