Purchasing Power Parity is an important theory at the basis of a large number of economic models. However, the implication derived form the theory that real exchange rates must follow stationary processes is not conclusively supported by empirical studies. In a recent paper, Serletis and Gogas (2000) show evidence of deterministic chaos in several OECD exchange rates. As a consequence, PPP rejections would be spurious. In this work, we follow a two-stage testing procedure to test for non-linearities and chaos in real exchange rates, using a new set of techniques designed by Webber and Zbilut (1994), under the denomination of Recurrence Quantification Analysis (RQA). Our conclusions differ slightly from Serletis and Gogas (2000), but they are also supportive of chaos for some exchange rates.