This dissertation poses the question of whether there is a relationship between the speed of convergence of globalisation and the speed of convergence of GDP per capita. Firstly, the concepts of globalisation and real convergence and their relationship are thoroughly explained from both the theoretical and empirical point of view. And secondly, the answer to the question comes in the form of beta and sigma convergence analysis of this relationship. Thirdly, the analysis splits the countries into two groups (developed and developing countries) and finds interesting but ambiguous results in their comparison. Finally, in order to correctly interpret the results of absolute and conditional beta and sigma convergence, their theoretical and empirical overview is discussed in depth. The dissertation concludes by providing some answers to the initial question for every particular analysis. Namely, it shows that this relationship is indeed very ambiguous.