Abstract The controversy about the monetary regime of the EC between the Britain and the other member countries made economists to study currency competition and currency substitution widely. This dissertation constructs a one-good, two-currency Brock model in discrete time. In the determinate model, we show the Gresham’s Law results as those in Weil’s. And we demonstrate the existence and uniqueness of a class of first-order Markov stationary sunspot equilibria. The existence of sunspot equilibria expresses another situation of currency competition that future situations may depend on the possibility of people’s expectations, not the growth rates of currencies and tries to provide another explain for the phenomena above.Britain and the other member countries made economists totudy currency competition and currency substitution widely .his dissertation constructs a one - good , two - currencyrock model in discrete time . In the determinate model , wehow the Gresham' s Law results as those in Weil's . And weemonstrate the existence and uniqueness of a class of firstorder Markov stationary sunpot equilibria . The existencef sunspot equilibria expresses another situation of currencyompetition that future situations may depend on the possibi-ity of people' s expectations , not the growth rates of cu -rencies and tries to provide another explain for the pheno -ena above .