Abstract. This paper examines price and in¯ation convergence between three European countries (Italy, Spain and the U.K.) and a European average and, alternatively, between them and Germany from the beginning of the 80's.For this purpose the long-run stochastic relationships on prices derived from the convergence criteria agreed in the Maastricht Treaty are analyzed. In order to do this, some recent unit root tests have been applied as well as timevarying parameters models.The results reject the long-run convergence hypothesis in all the cases but allow us to accept the existence of catching-up with the European average and Germany in some cases depending on the nature of the prices and on the countries considered.