This paper investigates ‘exterminous hypertime’, a model of time travel in which time travellers can change the past in virtue of there being two dimensions of time. This paper has three parts. Part one discusses the laws which might govern the connection between different ‘hypertimes’, showing that there are no problems with overdetermination. Part two examines a set of laws that mean changes to history take a period of hypertime to propagate through to the present. Those laws are of interest (...) because: (i) at such worlds, a particular problem for non-Ludovician time travel (‘the multiple time travellers’ problem) is avoided; and (ii) they allow us to make sense of certain fictional narratives. Part three discusses how to understand expectations and rational decision making in a world with two dimensions of time. I end with an appendix discussing how the different theories in the metaphysics of time (e.g., tensed/tenseless theories and presentism/eternalism/growing block theory) marry up with exterminous hypertime. (shrink)