The recent progress in spatial econometrics offers a number of estimators for models that treat spatial dependence explicitly but techniques for handling spatial dependence appear to be essentially confined to crosssectional studies. Despite the fact that dynamic panel models have been the object of recent important developments, the econometric analysis of spatial and dynamic panel models is at an early stage. In this context, the aim of this paper is to review the different methods used in the literature, for such space-time data sets, and to suggest two strategies in order to estimate spatial dynamic panel using GMM. The first is to extend the moment restrictions of Arellano and Bond estimator for spatial autoregressive dynamic panel. The second allows for spatial dependence in the error process in calculating the optimal weighting matrix at the second step of the Arellano and Bond estimator. These strategies are carried out to estimate the convergence of European regions during the last 25 years.