Zahavi's `handicap principle' proposes that females prefer males with handicaps (mating characters that reduce survival chances) because handicaps are indicators of heritable viability. It is shown here that there are conditions under which the `handicap principle' causes the runaway exaggeration of male handicaps and female mating preferences. The conditions required are (a) that the fitness effects of the handicap and `viability' genes combine non-multiplicatively (Zahavi's handicap), and/or (b) that the handicap should directly reveal the presence or absence of genes for high viability (the revealing handicap). The `handicap principle' by itself cannot initiate increases in female preference when the handicap is rare. It only works when a threshold value of female preference is exceeded, and Fisher's feedback process operates. When Fisher's feedback process occurs alone, a line of equilibria exists, where for each intensity of female preference there is a corresponding equilibrium development of the male mating character. When the `handicap principle' also operates, the internal line of equilibria is eliminated, and only boundary equilibria persist (i.e. fixation or loss of the handicap). All populations at what were previously internal equilibria, or in which the intensity of female preference is above threshold, increase in a runaway to fixation of the handicap; therefore, handicapping male mating characters are more likely to be exaggerated when they are also indicators of viability.