In this paper we investigate empirical specification of smooth transition error correction models (STECMs). These models can be used to describe linear long-run relationships between nonstationary variables where adjustment towards equilibrium is nonlinear and can depend on exogenous variables. The various steps involved in specifying an appropriate model are discussed for a monthly bivariate interest rate series for The Netherlands. Using simulations we first establish that standard (linearity-based) cointegration tests can be used to examine joint long-run properties. Second, we apply various tests for nonlinearity to decide on an appropriate function for the adjustment of disequilibrium errors. When we estimate an STECM, we find indications that nonlinearity is due to only two observations. We investigate the relevance of these data points by applying robust tests for linearity and by considering less aggregated, i.e. weekly, data. We conclude with some suggestions for practitioners.