The importance of chance variation in mate-encounter rates, and of sex differences in times, in generating sexual differences in the variance in success of polygamous species has been the subject of some discussion. Sutherland (1985a,b), for example, treated behavior as a time-budget problem within optimal foraging theory (foraging for mates) and noted a major difference in mating for males and females. Included in time are all matingrelated processes that reduce the ability of an individual to search for additional mates. Males typically have much shorter times than do females, which often delay remating until, for example, the end of an extended period of parental care. Sutherland (1985a) argued that random in a population in which the sexes differ in the length of the period before remating (hereafter, latency) results by itself in the observed asymmetry in the strategies of the sexes and that there is no need to invoke male-male competition or female choice. Bateman's (1948) data showing a higher variance in the success of Drosophila melanogaster males were consistent with such a random-mating model. In this paper, we develop Markovian models in which males and females are distinguishable, following Sutherland (1985a), by their differing postmating latencies. Using these models, we consider two problems. The first deals with the consequences of chance variation in life history for individual strategies. We analyze the evolutionarily stable strategies (ESS) for mate choice by males and females encountering a random stream of potential mates with two qualities. We answer the question of the evolution of choosiness as a function of survival rate, the duration of postmating latency, the probability of encountering potential mates, the proportion of high-quality potential mates, and the difference in quality of the potential mates. The second problem concerns the implications of chance variation in lifetime success (LMS) for the theory of sexual selection. We calculate LMS means and variances for males and females under a model of constant risk of death per unit of time. We examine a model in which the variance in