According to New Growth Theory one can not rely on the convergence mechanisms inherent in traditional neoclassical constant returns to scale models. Convergence as well as divergence is possible, in general, depending on the assumptions about technology, factor mobility and ease of knowledge diffusion. The paper shows by a two-regions endogenous growth model under what conditions divergence, convergence or a stable centre-periphery structure emerge. The model allows for different degrees of knowledge diffusion as well as for different degrees of labor and capital mobility. The paper also evaluates dynamic market equilibria with respect to allocative efficiency. It is shown that the market solution tends to be under-agglomerated, except for parameter constellations generating particularly low agglomeration forces. If agglomeration forces are low enough, no concentration emerges, and this is also socially desirable. For higher agglomeration forces, however, concentration becomes desirable though the market may not bring it about or brings it about to an insufficient degree only.