Countries' scientific systems are a key element of the knowledge economy. This paper explores the convergence pattern of the scientific systems of a wide range of countries around the world during the period 2003-2016. Drawing on data on national scientific production from a sample of 121 developed and developing countries, the log t test methodology has been used to detect whether there has been an overall convergence in knowledge creation among countries, if they have converged in clubs, or if there have been divergent countries. The results show the absence of overall convergence; on the contrary, the presence of five groups of countries that converge together has been detected, showing differentiated knowledge production growth trajectories among them. A divergent country (UK) has also been identified. Furthermore, the paper examines the scientific structure of these clubs and the countries that form them, identifying in which scientific fields the scientific systems of countries have a comparative advantage/disadvantage in relation to the world average.