The authors show that spatial dependence and spatial heterogeneity matter in the estimation of the β-convergence process among 138 European regions over the 1980 to 1995 period. Using spatial econometrics tools, the authors detect both spatial dependence and spatial heterogeneity in the form of structural instability across spatial convergence clubs. The estimation of the appropriate spatial regimes spatial error model shows that the convergence process is different across regimes. The authors also estimate a strongly significant spatial spillover effect: the average growth rate of per capita GDP of a given region is positively affected by the average growth rate of neighboring regions.