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Negative senescence is characterized by a decline in mortality with age after reproductive maturity, generally accompanied by an increase in fecundity. Hamilton (1966) ruled out negative senescence: we adumbrate the deficiencies of his model. We review empirical studies of various plants and some kinds of animals that may experience negative senescence and conclude that negative senescence may be widespread, especially in indeterminate-growth species for which size and fertility increase with age. We develop optimization models of life-history strategies that demonstrate that negative senescence is theoretically possible. More generally, our models contribute to understanding of the evolutionary and demographic forces that mold the age-trajectories of mortality, fertility and growth.