Two quantitative models of the handicap principle are presented which incorporate phenotypic plasticity, i.e. flexibility in the expression of a handicapping trait. The first model ("multiplicative model") applies to instances in which greater development of the trait improves male mating success while lowering survival. Two examples treated are antler size in deer and tail length in birds. The second model ("additive model") applies to instances in which an individual performs a display which, though potentially costly, may nevertheless deter an opponent (or predator). Stotting in gazelles and roaring among stags illustrate application of the second model. The conclusions of the models are that optimal development of the handicap will correlate positively with the "condition" (e.g. the nutritional state) of the individual. This allows a female (or predator) to benefit by choosing (or avoiding) a mate (or prey) of better condition on the basis of the size of the handicap alone. The benefit to the choosing individual is discussed. The multiplicative model appears quite robust. Most importantly, in nearly all plausible situations, the model indicates that those individuals displaying the greatest handicap will at the same time survive best, and vice versa. On the other hand, the additive model appears valid only under a narrow range of conditions; therefore caution is advised in applying this model. The models suggest conditions which favor the evolution of phenotypic plasticity and indicate why, in nature, survival and fecundity (e.g. mating success due to intrasexual or intersexual selection) are often positively correlated.