This paper develops a two-sector model of growth where agriculture is considered explicitly. Key features of the model include: the reliance of agricultural production on a fixed but degrading resource base, the use by the farm sector of industrially produced inputs and differing rates of technological progress in the two sectors. On the demand side, the low income elasticity for food as well as the life-sustaining function of food consumption are recognized. In this simplified framework, the sustainability of growth can be related to the existence of a steady state reflecting the ability of the economy to feed its population. This property is used to identify the characteristics within and outside of agriculture conducive to the sustainability of a land-constrained economy. The empirical application identifies sub-Saharan Africa as the region of the world facing the most important challenges in terms of sustainability. The second part of the paper makes use of the transitional properties of the model to analyse the relationship between agricultural productivity and growth performance. For a closed economy, the model unambiguously supports the view that high agricultural productivity is conducive to fast growth and industrialization. Once the country is allowed to trade, however, the relationship becomes more complex, but a numerical experiment illustrates how trade liberalization can accelerate the growth of a country poorly endowed in agricultural resources.