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Advances in image super-resolution (SR) have recently benefited significantly from rapid developments in deep neural networks. Inspired by these recent discoveries, we note that many state-of-the-art deep SR architectures can be reformulated as a single-state recurrent neural network (RNN) with finite unfoldings. In this paper, we explore new structures for SR based on this compact RNN view, leading us to a dual-state design, the Dual-State Recurrent Network (DSRN). Compared to its single-state counterparts that op-erate at a fixed spatial resolution, DSRN exploits both low-resolution (LR) and high-resolution (HR) signals jointly. Recurrent signals are exchanged between these states in both directions (both LR to HR and HR to LR) via de-layed feedback. Extensive quantitative and qualitative eval-uations on benchmark datasets and on a recent challenge demonstrate that the proposed DSRN performs favorably against state-of-the-art algorithms in terms of both mem-ory consumption and predictive accuracy.