Abstract We develop formulas for testing UIP with Markov-switching VAR models in which all the parameters are regime-dependent. The formulas are extensible to other contexts where rational expectations intervene in non-linear bivariate Switching-VAR models of the type considered here. The testing procedure is implemented on several samples of data for the post-1973 free floating period (Spain–United Kingdom, Germany–United States). Contrary to most of the received evidence – mainly obtained with linear and therefore probably misspecified models – the results for these developed countries are favourable to the UIP, especially in the case of Spain–United Kingdom after the entrance of Spain in the EU. The econometric methodology proposed offers therefore an explanation for the empirical UIP puzzle.