This paper introduces the appropriate econometric methodology and statistical tests to evaluate the spatial and sectoral stability of the labour productivity convergence process of 145 European regions over 1975–2000. Our results display significant σ‐convergence only in aggregate labour productivity and in the services sectors among peripheral regions. We also show that omitting spatial effects leads to biased measures of σ‐convergence. We then estimate a pooled β‐convergence model including spatial autocorrelation and sectoral differentiation. Spatial and sectoral stability tests reveal which sectors display a convergence process and in which regime they are located.