Summary: In formalizing temporal reasoning, should a proposition be allowed to change its truth value infinitely often over a finite period of time? It has been widely felt that for many types of proposition this phenomenon, which following Hamblin we call ‘intermingling’, should be outlawed. In this paper we systematically examine the varieties of intermingling, distinguishing intermingling over an interval from intermingling at an instant. We survey the axioms that have been proposed in the literature to rule out intermingling, and determine precisely which varieties of intermingling are ruled out by which axioms. We distinguish ‘weak’ non-intermingling principles, which only rule out one or two forms of intermingling, from ‘strong’ non-intermingling principles which rule out all or most forms of intermingling. We show that none of the first-order solutions in the literature suffices to rule out all forms of intermingling, though a second-order solution can do so.