This research studies the long memory behavior of daily returns of Chinese Yuan (CNY), Indonesian Rupiah (IDR) and Taiwanese Dollar (TWD). Fractionally integrated models, ARFIMA and FIGARCH, were used to investigate the long memory property in returns and volatility, respectively. The results reveal that CNY and TWD exhibit long memory property in returns. All the three currencies exhibit long memory in volatility. The study further investigates the long memory dynamics in returns and volatility simultaneously using joint ARFIMA-FIGARCH model. The results indicate that there exists dual long memory in CNY and IDR which is better captured by ARFIMA-FIGARCH model under the assumption of skewed student-t distribution. The presence of long memory in returns of CNY and TWD implies that their behavior is predictable and hence, refutes the efficient market hypothesis. Likewise, the evidence of long memory in volatility reveals uncertainty or risk in the behavior of two exchange rates.