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Using the Geweke–Porter-Hudak test, we find evidence of long memory in exchange-rate data. This implies that the empirical evidence of unit roots in exchange rates may not be robust to long-memory alternatives. Fractionally integrated autoregressive moving average (ARFIMA) models are estimated by both the time-domain exact maximum likelihood (ML) method and the frequency-domain approximate ML method. Impulse-response functions and forecasts based on these estimated ARFIMA models are evaluated to gain insight into the long-memory characteristics of exchange rates. Some tentative explanations of the long memory found in the exchange rates are discussed.