We introduce a neural network layer API and library for sequence modeling, designed for easy creation of sequence models that can be executed both layer-by-layer (e.g., teacher-forced training) and step-by-step (e.g., autoregressive sampling). To achieve this, layers define an explicit representation of their state over time (e.g., a Transformer KV cache, a convolution buffer, an RNN hidden state), and a step method that evolves that state, tested to give identical results to a stateless layer-wise invocation. This and other aspects of the SequenceLayers contract enables complex models to be immediately streamable, mitigates a wide range of common bugs arising in both streaming and parallel sequence processing, and can be implemented in any deep learning library. A composable and declarative API, along with a comprehensive suite of layers and combinators, streamlines the construction of production-scale models from simple streamable components while preserving strong correctness guarantees. Our current implementations of SequenceLayers (JAX, TensorFlow 2) are available at https://github.com/google/sequence-layers.