Evidence that real exchange rate dynamics can be described using models which exhibit nonlinear mean reversion has been mounting over the past several years. This paper attempts to better understand the shape of real exchange rate nonlinearity through the use of the smooth transition autoregressive (STAR) model and the newly proposed skewed generalized error (SGE) transition function. The advantage of this transition function is that is nests popularly used transition functions through simple parameter constraints. This allows the use of nested model selection tests. It is shown that more flexible transition functions are preferred in many cases over the commonly used exponential transition function. The results suggest that most of the real exchange rates studied in this paper are better described by discrete threshold models rather than STAR models.