The paper analyses the contribution of efficiency as a mechanism of labour productivity convergence, taking as the unit of analysis the Spanish regions in the period 1964-1993. Using the stochastic frontier approach, a translogarithmic production function is estimated for the different sectors of the Spanish regional economy, demonstrating on this basis the existence of substantial differences in efficiency between sectors as well as between regions. With regard to convergence, the results obtained indicate that at aggregate level the convergence observed in labour productivity is explained by the faster growth of the capital-labour ratio of the initially poorer regions and the contribution of technical change and the efficiency, hence by the convergence of TFP. However, the information by sectors shows different results. Thus, on the one hand, the importance of the convergence in production per employee is seen in all sectors except agriculture and, on the other it is observed that technical change is a factor of convergence in all sectors but construction, and, qualitatively, the contribution of technical change is greater than the contribution of efficiency. By sectors, technical change contributed significantly to labour productivity convergence in agriculture, but the faster growth of the capital-labour ratio of the rich regions acted as a mechanism of divergence, completely counteracting the technological catching-up effect. It is further concluded that, as well as the contribution of the accumulation of factors, the positive evolution of efficiency in the poorest regions favoured convergence in the construction and industry sectors, whereas technical progress was decisive in industry and the services sectors.