IN THIS PAPER we examine the concept of irreducibility in the von Neumann model, as defined by Gale [2, Ch. 9]. Since this property corresponds to a condition on the types of production in the model, we term it technological irreducibility. We show that there is a dual concept, which we call economic irreducibility, involving a condition on the price structure. The wellknown von Neumann indecomposability assumption is shown to have a very simple relationship to the property of economic irreducibility. We also show how to generalize certain results from the Perron-Frobenius theory of irreducible non-negative square matrices to the case of an irreducible von Neumann model.