Attention to issues of inequality and convergence has become a topic of considerable interest in both developing and developed economies. The purpose of this paper is to study empirically the evolution of the disparities between more than 360 Maghreb regions considering spatial dependence and to explore a non-parametric approach for characterizing convergence of GDP per capita. This study utilizes growth theory as the theoretical foundation to explore the convergence hypothesis. The methodology consists of identifying the shape of the long-run spatial associations through the use of Markov chains which make it possible to derive a unique stationary distribution related to the transition matrix. The results of the analysis indicate the persistence of regional disparities and the importance of geography to explain the global convergence process with positive spatial spillover effects. The proportion of high-income regions surrounded by similar regions has significantly increased detrimentally to the other spatial associations. This non-parametric approach complements the standard parametric method (absolute and conditional beta-convergence) which shows that the slow convergence process can be accelerated by beneficial spatial interaction effects. These results have strong policy implications with regard to national and territorial policies in these countries.