How must experience of time be structured in time? In particular, does the following principle, which I will call inheritance, hold: for any temporal property apparently presented in perceptual experience, experience itself has that same temporal property. For instance, if I hear Paul McCartney singing ‘Hey Jude’, must my auditory experience of the ‘Hey’ itself precede my auditory experience of the ‘Jude’, or can the temporal order of these experiences come apart from the order the words are experienced as having? A number of recent authors (Phillips Experience and Time, ‘The Temporal Structure of Experience’, Soteriou ‘Perceiving Events’, Hoerl ‘“A Succession of Feelings, in and of Itself, is Not a Feeling of Succession”’, Rashbrook) claim, to paraphrase Martin (399), that inheritance best characterises how our temporal experience seems to initial reflective intuition. For this reason, Phillips takes the principle to form part of our naïve view of temporal experience. An opposing group of theorists object that inheritance is subject to empirical counter-example. This article surveys such challenges. Section 2 considers Grush's case against inheritance based on postdiction. Section 3 examines Watzl's anti-inheritance argument based on silencing effects. Finally, Section 4 explores a number of alleged counter-examples proposed by Lee (‘Temporal Experience and the Temporal Structure of Experience’). Section 1 provides essential background to the debate.