The extent to which exchange rates of four major currencies against the Greek Drachma exhibit long-term dependence is investigated using a R/S analysis testing framework. We show that both classic R/S analysis and the modified R/S statistic if enhanced by bootstrapping techniques can be proven very reliable tools to this end. Our findings support persistence and long-term dependence with non-periodic cycles for the Deutsche Mark and the French Franc series. In addition a noisy chaos explanation is favored over fractional Brownian motion. On the contrary, the US Dollar and British Pound were found to exhibit a much more random behavior and lack of any long-term structure.