This paper presents an extended model of cumulative growth in which the effects of innovation and catching-up are considered. The effect of innovation adds another source of cumulative growth to that of the traditional models and allows for the consideration of the importance of non-price factors as determinants of international competitiveness. Catching-up, on the other hand, is the major force leading to convergence in productivity due to the effect of the diffusion of technology. The model allows for analysing whether cumulative forces may lead to stable growth and whether this solution generates convergence in productivity levels. The structural model is then tested for a set of OECD countries over the period 1965 to 1994 and the results are used for carrying out the comparative dynamics. The results support the view that both the Verdoorn-Kaldor mechanism, and the induced effect of innovation on export performance, are important cumulative forces that interact with the effect of catching-up towards a convergent pattern of growth.