The demographic model of senescence described here provides an answer to the question, "Why should senescence evolve?" Most generally stated, the answer is that senescence should be expected to evolve if its negative effect on the rate of natural increase of a nonsenescent population is sufficiently offset by the early appearance of an advantageous characteristic. This is a nonadaptive point of view in the sense discussed by Kirkwood (1985) and by Kirkwood and Cremer (1982). It corresponds more closely to Medawar's (1952) position than to Weisman's (1889). The demographically based model in which senescence is represented by sudden death supplies an explanation which is simple and credible for the evolution of senescence. It supports the following specific conclusions: 1. The introduction of sudden death (case 2) in a nonsenescent population otherwise subject only to randomly occurring death (case 1) is, by itself, disadvantageous from the standpoint of natural selection. 2. However the population may enjoy a net selective advantage if the disadvantage of sudden-death senescence is compensated by an appropriate improvement early in its life history, e.g., by a reduction in its presenescent death rate. 3. In the most extreme example possible, in which the presenescent death rate is zero and the survival curve is rectangular (case 3), the early improvement is associated with an increase in the degree of sensescence of the population, in its mean longevity, and in its average age at death. Thus natural selection can simultaneously favor both senescence and longevity. 4. Among populations in which the age of sudden death is balanced against the presenescent death rate in such a way that mean longevity is held constant (case 4), sudden-death senescence provides selective advantage relative to a nonsenescent population (case 1). Up to the point at which the survival curve becomes rectangular, the earlier the age at which sudden-death occurs, the greater the selective advantage. Similar conclusions were reached earlier with respect to forms of senescence which take effect more gradually than the sudden-death mechanism postulated here. 5. Populations in which the age of sudden death is balanced against the presenescent death rate in such a way that the average age at death is held constant (case 5) are selectively neutral with respect to a nonsenescent population (case 1). Thus a reduction in mortality at a nearly age can compensate for the sudden death of the whole population at an advanced age because so few individuals in the nonsenescent population survive to reproduce when old.