For the last fifty years, countries in Asia and elsewhere witnessed a surge in aggregate savings per capita. Many empirical studies attribute this trend to the highly significant increases in life longevity of the populations of these countries. Some argue that the rise in savings is shortrun, to be eventually dissipated by the dissaving of the elderly, whose proportion in the population rises along with longevity. This paper examines whether these conclusions are supported by economic theory. A model of life cycle decisions with uncertain survival is used to derive individuals' consumption and chosen retirement age response to changes in longevity from which changes in individual savings are derived. Conditions on the age-profile of improvements in survival probabilities are shown to be necessary in order to predict the direction of this response (the uneven history of age specific improvements in longevity is recorded by Cutler (2004)). Population theory (e.g. Coale (1952)) is used to derive the dependence of the steady-state population age density on longevity. This, in turn, enables the explicit aggregation of individual response functions and a comparative steady-state analysis. Sufficient conditions for a sustainable positive effect of increased longevity on aggregate savings per capita are then derived. These conclusions pertain to an economy with a competitive annuity market. Public Social Security systems provide some annuitized benefits, but in order to provide an adequate consumption flow during retirement individuals typically have to supplement these benefits with annuities purchased in the private market. The absence of such market compels individuals to leave unintended bequests, whose size depends on the (random) age of death. While an increase in longevity raises individual savings for given endowments, it is shown that the effect on expected steady-state aggregate savings, taking into account the endogenous ergodic distribution of endowments, cannot be determined apriori.