This paper adopts a new approach to the problem of generalizing the properties of the two-by-two Heckscher-Ohlin model, asking whether we can obtain results which hold in very general models for dichotomous categories of commodities and factors. Using duality theory, some results of this kind are derived, which generalize certain properties of the Heckscher-Ohlin model to models which allow for any number of goods and factors, joint production, international factor mobility, and substitution between primary factors and intermediate inputs. The consequences of assuming sector-specific factors and equal numbers of goods and factors' are also examined.