There appear to be two sorts of doxastic attitudes, propositional beliefs in the traditional sense (belief that your shoes are tied) and Bayesian credences (degree of belief .998 that your shoes are tied). Deductive consistency and closure traditionally define coherence for belief.Probability theory traditionally defines coherence for degrees of belief. That leaves open the question how propositional and probabilistic beliefs should cohere with one another. We refer to that as the problem of doxastic coherence. We explicate doxastic coherence in terms of rationality constraints on doxastic correspondences that map propositional belief states to Bayesian credal states. Of particular interest is the principle that doxastic correspondences should preserve diachronic coherence. By way of application, we propose a concrete family of coherent doxastic correspondences. Furthermore, we show that the familiar Lockean proposal that one should believe the propositions that pass a credal threshold is incoherent in a number of important respects.