Theorists of contemporary international relations try to grasp a world of rapid change. No one seems sure of today's global politics, still less of what is to come. Views of the future proliferate, books telling us how the 21st century will look are in great demand and, one imagines entirely contrary to intention, politicians and policymakers are free to select, a la carte, those ideas that best conform to their preferences and prejudices. These two volumes fit within the ever-expanding realm of international-relations soothsaying but have quite different things to offer.

The first, a collection of essays assembled largely from the 2003 Miliband Lectures at the London School of Economics, presents a smorgasbord of competing visions of the future. The second is the work of a single author, Barry Buzan, who covers much ground through the catholic use of competing theories. The first is likely to appeal to a generalist, a reader of the journal Foreign Affairs or an undergraduate student in international relations, history or politics. The second is more complex, more terminological, tied tightly to the canon, and is likely to appeal to advanced students and researchers who specialise in America's foreign policy and who work in international relations departments.

As might be expected, there is little agreement about America's place in the world, where it might be tomorrow and how either position differs from where it should be: a point the editors of American Power in the 21st Century note in their introductory essay. Sketching four potential future states - empire, global democracy, collective security, balance of power - they provide outer limits of possible future states within which contributors comfortably fall. But these outliers are so grand that there is ample room for disagreement: over the nature of US power, how secure it is, whether dominance requires, or even permits, multilateralism, whether "soft" or "hard" power provides the best return on political investment and a host of other topics. Reading the book from cover to cover produces a gaggle of voices and plenty of material for classroom debate. On the other hand, contributors make assertions they are already well known for. In some cases, their positions have not changed since the Cold War.

No one familiar with these individuals is likely to be surprised by what is found here: indeed, Robert Kagan's essay is a direct lift of his infamous Policy Review article "Power and weakness". For this reason, the most stimulating contributions come from outside the Atlantic mindset, particularly Zhiyuan Cui's analysis of the Chinese perspective on the Bush doctrine. (Cui argues that a realist China sees Clinton and Bush as part of a post-Cold War continuity, and has responded with efforts to counterbalance US power in Asia as well as the European Union.) Someone seeking to survey the state of play in international relations theory today would do well to look here; someone looking for new insights might look elsewhere.

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Buzan's goal is to construct a model for today's international system based on a qualified version of neorealist polarity theory. By bolting on ideas of collective identity and a multi-tier system of classification, Buzan argues, one can explain today's curious political environment. We are in a "1+4" world (one superpower, four great powers): a plurality lacking a majority. This model places a greater premium on great power identity than neorealists would accept. It suggests that the system may prove durable, and that the most probable alternative state in the near term is a world of no superpowers and multiple great powers, something the author considers probably dangerous. The argument is rigorous and intriguing - revealing both for the limits and possibilities of applying structural models to grand strategy - although the policy recommendations in the final part of the book are less than surprising.

Given today's uncertainty, the diversity in these books is to be welcomed. Most contributors, however, agree that the key determinant of change will be US foreign policy. Given that the signal event of the era to date was committed by a few Saudi Arabians, this is in itself a position that hindsight may come to challenge.

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Alex Goodall lectures in American history at Edinburgh University.