This paper develops a two-sector growth model incorporating the essential distinguishing features of agriculture, including the reliance of production on a natural resource base as well as on industrially produced inputs, the low income elasticity of demand for food and the life-sustaining function of food consumption. In this framework, the ability of an economy to supply an adequate supply of food to a growing population can be related to the existence of a steady state. This property is used to define a simple analytical criterion upon which to assess the long-term food situation of a closed economy. This sustainability condition relates all the dynamic parameters of the economy: rates of technological change in the two sectors, rate of population growth and rate of land degradation. The condition is used to highlight the technological characteristics in agriculture conducive to sustainability and to assess empirically the food situation of a number of countries. Although no global food crisis appears to be looming ahead, the data suggest that sub-Saharan Africa is likely to increase its food dependence in the future.