In this paper we develop a model of international specialisation and catching-up which combines Ricardian and Schumpeterian features. Catching-up patterns are endogenised by FDI flows which react to industry specific unit rents and thus enforce convergence dynamics. This generalises the Gerschenkronian idea of the "advantage of backwardness" to be applied at a disaggregated level and explains the empirically observed pattern that some countries converge faster in the high tech sectors where the initial gap is larger. Depending on the productivity, wage and profits dynamic there may be "comparative advantage switchovers" in which a catching-up economy turns its competitive advantage towards medium-to hightech areas. We investigate in which way labour market dynamics, productivity catching-up and investment patterns all combine to determine the evolution of the international division of labour. Further we point also to the impact on labour demand and wage structures (between skilled and unskilled workers) both in the lead and the catching-up economies.