In this paper, we consider inflation rate differentials between seven Central and Eastern European Countries (CEECs) and the Eurozone. We test for convergence in the inflation rate differentials, incorporating non‐linearities in the autoregressive parameters, fractional integration with endogenous structural changes, and also consider club convergence analysis for the CEECs over the period 1997 to 2015 based on monthly data. Our empirical findings suggest that the majority of countries experience non‐linearities in the inflation rate differential; however, there is only evidence of a persistent difference in some countries. Complementary to this analysis we apply the Phillips and Sul (2007) test for club convergence and find that there is evidence that most of the CEECs converge to a common steady state.