After the devastation of the Second World War, the federal units of the former Yugoslavia were on their way to catching up with the Western Europe, with different degrees of success. In fact, Yugoslavia was considered a success story among the socialist economies due to its specific self-management system. Nevertheless, among the Federal units that later became independent states, regional differences in development level increased, in spite of the proclaimed policy to narrow them. Enough time has passed since the wars of the breakup and the economic transition to check if this divergence is continuing under a capitalist market system, now that all the countries are on the path to the European Union (EU) accession. The paper tests the convergence hypothesis among the states of the former Yugoslavia in terms of Human Development Index (HDI), as a more complex indicator of country development than GDP per capita. The results of two different approaches to test for the presence of β (beta) and σ (sigma) convergence suggest that the gap between the states of former Yugoslavia is closing, albeit at a slow rate. Given that convergence is slow, the active EU policies aimed at hastening the accession of the currently non-member states of the former Yugoslavia would accelerate the process.