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During the 20th century hunger has become a problem of poverty amidst plenty rather than absolute food scarcity. The question is whether this will remain so or whether the hunger of the poor will once more be exacerbated by rising food prices. In this paper we discuss biophysical conditions, social forces and non-linear interactions that may critically influence the global availability of food in the long term. Until 2050, the global demand for primary phytomass for food will more than double, while competing claims to natural resources for other purposes (including biobased non-foods] will increase. A sober assessment of the earth's biophysical potential for biomass production, which recognizes competing claims and unavoidable losses, suggests that this is in itself still large enough for accommodating this rising demand. However, the exploitation of this biophysical potential proceeds through technical paradigms that set a relative maximum to food production. In addition, socio-economic mechanisms make the food economy run up against a ceiling even before this maximum is reached. As a consequence, current developments may well entail a new trend change in international markets. These developments include the depletion of land and water reserves, the stagnation of the potential yields of major crops, the rise in energy prices, and the way in which systemic socio-economic factors lead to a strong underutilization of production possibilities in the developing world. Given these conditions, the avoidance of steep rises in food prices may depend on the timely relaxation of socio-economic constraints in developing countries and on timely breakthroughs in sustainable yield increases, biorefinement and non-farm production systems. Myopic expectations make it doubtful whether spontaneous market forces will provide the necessary incentives for this, which may be reason for societal actors to consider the need for more active policies.