This paper presents an essay on empirical testing procedure for economic convergence. Referring to the unit root test proposed by Moon and Perron (2004), we proposed a modified Evans (1996)testing procedure of the convergence hypothesis. The advantage of this modified procedure is that it makes p… ossible to take into account cross-sectional dependences that affect GDP per capita. It also allows to take into account structural instabilities in these aggregates. The application of the procedure on OECD member countries and CFA zone member countries leads to accept the hypothesis of economic convergence for these two groups of countries, and it shows that the convergence rate is significantly lower in the OECD sample. However, the results of the tests applied to the Global sample composed by all countries in these two samples conclude a rejection of the convergence hypothesis.