The importance, legitimacy and role of second-order probabilities are discussed. Two descriptive models of the use of second-order probabilities in decisions are presented. The results of two empirical studies of the effects of second-order probabilities upon the rank orderings of bets are summarized briefly. The bets were of three basic types and involved a wide variety of first- and second-order probabilities as subjectively assessed by the subjects. Support was obtained for the assumption that the majority of subjects make use of the one model or the other. It is suggested that greater attention should be paid to second-order probabilities, both from a normative and descriptive standpoint.