SECONDARY sexual characters are highly variable both within(1) and between species(2-6). Closely related species often differ markedly in sexual morphology but hardly at all In non-sexual traits(2-5). Here we show that Fisher’s runaway process of sexual selection is intrinsically unstable and naturally leads to continual change in sexual traits. Runaway leads to semi-stable exaggeration of female preference for a malt sexual character, followed by a slow decay of both traits until runaway is triggered again In a different direction. The process then repeats itself resulting in continual change in male sexual traits through time. Allopatric populations are thus expected to diverge without drift or substantial changes in selective pressures. If there is significant mutation bias acting on the male trait, continual change stops and a stable equilibrium appears. Such an outcome is more likely when exaggeration of the male sexual trait signals good genes.