A variety of avian taxa contain groups with 'reversed' (i.e. males smaller than females) sexual size dimorphism (Jehl and Murray 1986). Of all these taxa, its occurrence in the Falconiformes (hawks, eagles, falcons), the Strigiformes (owls) and the Stercorariidae (skuas) has received particular attention in the literature. These three independently evolved taxa have very different biologies but share predatory habits and, to a lesser degree, species in each show partial or complete sexual role specialization during breeding with males provisioning and females nest-tending. In other avian taxa reversed sexual dimorphism seems largely attributable to female-female competition for mates, but this explanation has seldom been applied to the hawks, owls and skuas (cf. Olsen and Olsen 1987). The diverse hypotheses that have been proposed (see reviews in Andersson and Norberg 1981, Mueller and Meyer 1985) are usually linked to the predatory nature of these birds. Many consider only a single selection pressure, operating only on one sex, without considering opposing selective forces. Arak (1988) has criticized this approach, pointing out that sexual dimorphism must arise from selection pressures for and against changes in body size acting differently on the two sexes (Ralls 1976, Price 1984). In this paper we use the framework for the evolution of sexual size dimorphism set out by Arak (1988) in an attempt to identify how different selection pressures acting on the two sexes could have resulted in the evolution of reversed sexual dimorphism in hawks, owls and skuas. We do not attempt a comprehensive review. Rather, we hope to convince the reader of the usefulness of Arak's approach: it easily accommodates the existing hypotheses, but helps make them more comprehensive, and it aids in identifying testable predictions not previously evident. We also modify and extend an existing hypothesis and show how, when used in the context laid out here, it provides explanations for broad patterns, as well as some of the exceptions, of sexual dimorphism in the groups considered. Hypothesis for reversed sexual dimorphism in predatory birds can be sorted into three categories, based on an evolutionary increase in female size, a decrease in male size, or a divergence in male and female size. The 'large female' hypotheses are (using the terminology in Andersson and Norberg's (1981) Table 1): the anticannibalism hypothesis, the male subordination hypothesis, the pair formation hypothesis, the egg size hypothesis, the incubation efficiency hypothesis, the nest protection hypothesis, the follicle protection hypothesis, and the starvation hypothesis. All these hypotheses assume that selection on breeding success favors large body size in females. In contrast, other hypotheses assume that the breeding success of pairs is enhanced when males are small. The 'small male', hypotheses are the energy savings hypothesis, the pyramid of prey hypothesis, the territorial defense hypothesis, and the courtship hypothesis. The 'dimorphic niche' hypotheses maintain that breeding pairs divergent in size are better able to exploit the prey base. They include the food competition and female supplementary feeding hypotheses. Descriptions of all these hypotheses, plus their sources, can be found in Andersson and Norberg (1981), with the exception of the starvation (see Lundberg 1986) and courtship (see Jehl and Murray 1986) hypotheses. Arak's (1988, see also Hedrick and Temeles 1989) framework for the evolution of sexual dimorphism considers natural selection acting on the survival and the reproductive consequences of body size. At the equilibrium body size in either sex, the fitness consequences of