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The main purpose of this thesis is threefold. Firstly, to bridge the gap between the growth models for the developed and the less developed economies; secondly, to bridge the very large gap between abstract growth theory and empirical analysis and thirdly, to provide a numerical analysis for optimal control policies. We tackled the first objective by constructing a two-sector growth model for a 'developing' economy, the first sector being the agricultural and the second sector the non-agricultural, by building on the assumptions of the dual development. The principal characteristics of our model arc the use of general production functions, the introduction of capital in the first sector, the bias in technological change between sectors and factors of production, the introduction of three income classes with three different propensities to save and the existence of wage differential between the two sectors which produces labour migration and which is decreasing over time. This model together with the presented demographic dualism, the mechanics of labour reallocation and the rate of urbanisation includes as special cases the models for the developed and the less-developed economies. The empirical validity of our model was our second objective. We studied the experience of the Greek economy for the, period 1950-72 and we estimated the structural parameters of the model using Cobb-Douglas production functions. This application permitted us to compare the behaviour of the ratios of economics of growth and the estimated parameters for the Greek economy between theory and reality. Finally, our last objective was to investigate numerically the sensitiveness of the optimal paths for the key variables of the economy under consideration by extending theoretically the descriptive growth model to a normative one and by applying in it the values of the parameters already estimated.