Methods, systems, and apparatus, including computer programs encoded on computer storage media, for augmenting neural networks with an external memory. One of the methods includes providing an output derived from the neural network output for the time step as a system output for the time step; maintaining a current state of the external memory; determining, from the neural network output for the time step, memory state parameters for the time step; updating the current state of the external memory using the memory state parameters for the time step; reading data from the external memory in accordance with the updated state of the external memory; and combining the data read from the external memory with a system input for the next time step to generate the neural network input for the next time step.