Résumé: This paper studies optimal stopping in continuous time, under non-exponential discounting. Our framework particularly captures decreasing impatience, a phenomenon well-documented in Behavioral Finance. Since non-exponential discounting induces time inconsistency, one should not naively employ optimal stopping times from classical theory, but rather look for equilibrium stopping policies under a game-theoretic setting. We provide a precise de_nition of subgame perfect Nash equilibriums in an intertemporal game among current and future selves. For time-inconsistent stopping problems, this is the _rst time a formulation of equilibrium is found in continuous time. Fixed-point iterations are carried out to search for equilibriums. Under appropriate conditions, the iteration is decreasing and indeed converges to an equilibrium. More importantly, the _xed-point iteration reveals a clear connection between a naive agent (who applies optimal stopping times) and a sophisticate one (who employs equilibrium policies). This connection is new in the literature of time-inconsistent problems.