In two studies, 4- to 6-year-olds were asked to name pictures of animals for the benefit of a watching hand puppet (the ongoing task) but to refrain from naming and to remove from view any pictures of dogs (the prospective memory [PM] task). Children also completed assessments of verbal ability, cognitive inhibition, working memory, and false-belief understanding (both studies), empathy (Study 1 only), and performance on false-sign tests that matched the false-belief tests in narrative content and structure (Study 2 only). Both studies found that inhibition and false-belief performance made unique contributions to the variance in PM, although in Study 1 the influence of inhibition was evident only when children needed to withhold naming. Study 2 further demonstrated that false-belief performance was the only reliable predictor of whether children remembered to return to the researcher an object that had been loaned to them prior to the picture-naming game. Both experiments uncovered moderate relations between PM and chronological age, but such relations were rarely significant after taking account of cognitive ability. We consider the implications of the findings for (a) current views regarding frontal/executive contributions to PM development and (b) the suggestion that the same brain network underlies various forms of mental self-projection, including envisioning the future and understanding the minds of other people. (Contains 8 tables.)