The aim of this paper is to study the dynamics of the real exchange rate deviations of G7 countries by capturing nonlinearity and long memory features. In this context, we used fractionally integrated STAR (FISTAR) models proposed by Van Dijk et al. (2002) [Van Dijk, D., Franses, P.H., Paap, R., (2002), A nonlinear long-memory model with an application to US unemployment, Journal of Econometrics, 110, 135-165.] for a case with an exponential transition function. Indeed, this study can take into account procedures characterized by several dynamic regimes and persistence phenomena. Empirically, the elements of both fractional long memory and threshold non-linearity are present for the real exchange rates of the G-7 countries against the US, notably in the EU countries.