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Abstract: In this paper I discuss two puzzles that concern the sense in which consciousness can be described as ‘continuous’. The first puzzle arises out of recent work by Dainton and Tye, both of whom appear to oscillate between ascribing the property of ‘continuity’ to the stream of experience, and ascribing it to the objects of experience. The second puzzle concerns the notion that the stream of consciousness could be in some sense unreal or illusory—a puzzle stemming from the thought that some of the brain processes underlying consciousness do not exhibit continuity. I argue that these problems can be solved by distinguishing between three possible bearers of the property of ‘continuity’—(1) the State of Consciousness, (2) the Stream of Experience, and (3) what is represented by experience—and two different senses of ‘continuity’—‘strict’ and ‘extreme’ continuity. I conclude by providing a positive account of the continuity of consciousness, according to which the State of Consciousness exhibits ‘strict’ continuity, and the Stream of Experience exhibits ‘extreme’ continuity.