This paper argues that versions of Samuelson/Cass-Yaari overlapping-generations consumption-loans models ought to be taken seriously as models of fiat money. The case is made by summarizing and interpreting what these models have to say about fiat money and by arguing that these properties are robust in the sense that they can be expected to hold in any model of fiat money. Two of the properties establish the connection between, on the one hand, the existence of equilibria in which value is attached to a fixed stock of fiat money and, on the other hand, the optimality of such equilibria and the nonoptimality of nonfiat-money equilibria. Other properties describe aspects of the tenuousness of monetary equilibria in such models: The nonuniqueness of such equilibria in the sense that there always exists a nonfiat-money equilibrium and the dependence of the existence of the monetary equilibrium on the physical characteristics of other potential assets and on other institutional features like the tax-transfer scheme in effect. Rather than being defects of these models, it is argued that this tenuousness is helpful in interpreting various monetary systems and, in any case, is unavoidable; it will turn up in any good model of fiat money. Still other properties summarize what these models imply about the connection—or, better, lack of such— between fiat money and private borrowing and lending (financial intermediation) and what they imply about country-specific monies.