This paper explains some implications of markov-process theory for models of mortality.We show, on the one hand, that an important qualitative feature which has been found in certain models --- the convergence to a ``mortality plateau'' --- is a generic consequence of the convergence to a ``quasistationary distribution'', which has been explored extensively in the mathematical literature.This serves not merely to free these results from some irrelevant specifics of the models, but also to offer a new explanation of the convergence to constant mortality. At the same time that we show that the late behavior --- convergence to a finite asymptote --- of these models is almost logically immutable, we also show that the early behavior of the mortality rates can be more flexible than has been generally acknowledged.We show, in particular, that an appropriate choice of initial conditions enables one popular model to approximate any reasonable hazard-rate data.This suggests how precarious it might be to judge the appropriateness of mortality models by a perceived consilience with a favored hazard-rate function, such as the Gompertz exponential.