Most studies of the efficiency of the foreign exchange market focus on a single maturity -- usually a one month exchange rate. However, one observes that forward contracts of many maturities are simultaneously traded in the foreign exchange market. The hypothesis that the foreign. exchange market uses all available information has implications for the joint behavior of forward exchange rates of various maturities. This paper theoretically and empirically examines these implications. The paper proposes an equilibrium theory of the term structure of the forward premium. By combining the theory of the term structure of (domestic and foreign)interest rates with the hypothesis of interest rate parity, a simple expression relating the six month forward premium to a geometric average of expected future one month forward premiums can be developed. By assuming that the one and six month forward premiums can be expressed as a bivariate stochastic process, one can derive an expression for the expected one month forward premium. The theory will then impose highly non-linear cross equation restrictions on the parameters of the model. Two methods of testing the validity of the restrictions are presented. The results indicate that the data are consistent with the theory for Germany and inconsistent with the theory for Canada.