The world population is expected to grow to 7.7 billion in 2020, from 5.3 billion in 1993 (UN, 1996). Although the latest population projections represent a slowdown from past estimates, the large absolute increase in population raises serious concerns about how food demand will be met in the next decades, especially in the context of a possibly stagnant or even decreasing stock of natural resources. These concerns have escalated sharply in recent years, in the face of dramatic increases in world cereal prices in 1996, combined with declining cereal stocks, and the simultaneous appearance of several widely read publications presenting the possibility of a starving world in the next century, unable to meet growing food demands from a deteriorating natural resource base (Brown, 1995; Tyler, 1995; Brown and Kane, 1994). In this paper, we examine the prospects for global food supply and demand for the year 2020, in the light of the two most often identified natural resource constraints, land and water. We first briefly summarize recent trends in area, yield and production for cereal crops, the key staple crops for most of the world, describe the IMPACT global food projections model and present an overview of food demand and supply projections. We then ask whether land and water constraints will pose serious threats to long-term cereal production growth. In particular, we assess the effects of land degradation and land conversion to urban uses on agricultural production and the effect of increasing water scarcity on future global food supply. For the latter assessment, we develop projections of global water demand until 2020 that are consistent with the underlying assumptions in the global food projections. We conclude with implications for land and water policy.