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End-to-end (E2E) automatic speech recognition (ASR) models, by now, have shown competitive performance on several benchmarks. These models are structured to either operate in streaming or non-streaming mode. This work presents cascaded encoders for building a single E2E ASR model that can operate in both these modes simultaneously. The proposed model consists of streaming and non-streaming encoders. Input features are first processed by the streaming encoder; the non-streaming encoder operates exclusively on the output of the streaming encoder. A single decoder then learns to decode either using the output of the streaming or the non-streaming encoder. Results show that this model achieves similar word error rates (WER) as a standalone streaming model when operating in streaming mode, and obtains 10% -- 27% relative improvement when operating in non-streaming mode. Our results also show that the proposed approach outperforms existing E2E two-pass models, especially on long-form speech.