We test for stochastic long-memory behavior in the returns series of currency rates for eighteen industrial countries using a semiparametric fractional estimation method. A sensitivity analysis is also carried out to analyze the temporal stability of the longmemory parameter. Contrary to the findings of some previous studies alluding to the presence of long memory in major currency rates, our evidence provides wide support to the martingale model (and therefore for foreign exchange market efficiency) for our broader sample of foreign currency rates. Any inference of long-range dependence is fragile, especially for the major currency rates. However, long-memory dynamics are found in a small number of secondary (nonmajor) currency rates.