Methods, systems, and apparatus, including computer programs encoded on computer storage media, for processing sequences using convolutional neural networks. One of the methods includes, for each of the time steps: providing a current sequence of audio data as input to a convolutional subnetwork, wherein the current sequence comprises the respective audio sample at each time step that precedes the time step in the output sequence, and wherein the convolutional subnetwork is configured to process the current sequence of audio data to generate an alternative representation for the time step; and providing the alternative representation for the time step as input to an output layer, wherein the output layer is configured to: process the alternative representation to generate an output that defines a score distribution over a plurality of possible audio samples for the time step.