In this paper we introduce threshold type nonlinearities within a single equation cointegrating regression model and propose a testing procedure for testing the null hypothesis of linear cointegration versus cointegration with threshold effects. Our framework allows the modelling of long run equilibrium relationships that may switch according to the magnitude of a threshold variable assumed to be stationary and ergodic and thus constitutes an attempt to deal econometrically with the potential presence of multiple long-run equilibria. The framework is flexible enough to accomodate regressor endogeneity and serial correlation. An important component of our analysis is also the development of a formal definition of the concept of threshold cointegration. Monte-Carlo simulations are used to show that the proposed procedures have good finite sample properties. <br><br> Keywords; nonlinear cointegration, multiple long run equilibria, thresholds, nonlinear dynamics, unit roots
