Endogeneous growth theory views externalities and particularly externalities associated with knowledge spillovers as the engine of economic growth. In some influential papers (e.g. Glaeser et al. 1992) it is argued that these knowledge spillovers do not transmit costlessly over space. Rather, location and geographic proximity matter. In the current paper a simple two country model is developed. Each country consists of a three-stage urban hierarchy: a central city (the core), a number of smaller cities and a rural hinterland. New technical knowledge originates in the core. The transmission of knowledge to the periphery and to the foreign country is impeded by geographic distance and national borders, inter alia. Depending on the relative importance of these obstacles different spatial patterns of knowledge diffusion emerge. The aim of the model is to analyze how different patterns of knowledge diffusion affect regional and national economic growth in the innovating country and in the imitating country.