BEYOND AMERICAN HEGEMONY The Future of the Western Alliance By David P. Calleo Basic Books. 288 pp. $20.95

BEYOND American Hegemony: The Future of the Western Alliance is a brilliant if somewhat pessimistic analysis. Its thesis is well summed up in its last few sentences: "The United States has become a hegemon in decay, set on a course that points to an ignominious end. If there is a way out, it lies through Europe. History has come full circle: the Old World is needed to restore balance to the New."

There is undoubtedly a power vacuum in the Western democracies, and only a united Western Europe has the breadth of interest and influence to help fill it. But Western Europe still lacks the self-confidence to assert its true power. Too many West Europeans fight shy of acknowledging even the raw statistics of Europe's relative power position, let alone their potential for influence. They do not like to be reminded, which David Calleo does with both skill and sensitivity, of the fact that the European Community has a combined gross national product larger than that of the United States or of the Soviet Union. That the European Community's total population is greater than that of either the Soviet Union or the United States. That although Western Europe has fewer men under arms and a smaller nuclear arsenal than either superpower, it nevertheless lies within its capability to expand conventional forces.

If negotiations for mutual and balanced force reductions fail, then Western Europe can make good any U.S. troop reductions in Europe made as part of a U.S. budget cut. Britain and France could take steps to buttress the U.S. nuclear guarantee in the wake of such troop reductions.

U.S. economic problems may be at the root of this power vacuum, but the American problems are, in fact, too glibly attacked in Europe. A lower U.S. dollar and a lower trade deficit would mean fewer exports from the other Group of Seven nations (Britain, Germany, France, Italy, Canada and Japan) to the United States. The job losses abroad from rapid abolition of the U.S. trade deficit would be considerable.

The six other nations in the Group of Seven have all lived securely behind the large U.S. defense budget. A sudden withdrawal of U.S. troops would be far more damaging to European unity than a phased withdrawal done with the full support of Western Europe. Western Europe should tell the United States that, to help eradicate the budget deficit, it will accept U.S. troop reductions. The current cost of U.S. force commitments to Europe for general purpose forces is around $150 billion a year. Cutting that over a period by a third would therefore make a $50 billion contribution to reducing the U.S. deficit, and it would have the least damaging effect on the world economy. It would also help if Canada lived up to its recent commitment to expand its defense budget.

It is not just in the strategic area but also in the economic area where American hegemony is under challenge. Obviously the dollar has lost market confidence. A more formal regime for exchange rates is clearly needed to cover the yen, the dollar and the deutschmark. The European Monetary System could be restructured, Britain could join the Exchange Rate Mechanism, a European Central Bank could be established and a new Group of Seven exchange rate mechanism could be created as part of a package for dealing with the U.S. deficit.

These are areas which David Calleo touches on, but they need to be given as great a priority as he gives to restructuring NATO. The world's, and particularly Europe's, perception of the superpowers -- not just the United States but also the Soviet Union -- has slowly, but quite fundamentally, changed. Both superpowers are looking inward to themselves, not outward to the world. Perestroika and glasnost are signs of weakness, not strength. The priority Gorbachev has chosen for the domestic economy is a priority that will also be forced on any incoming U.S. president. The Gorbachev-Reagan summit in Washington is one of two diminished superpowers. The two men are both in their different ways masters of the media, and this gives a false impression of power. The Nixon-Brezhnev relationship 15 years ago represented the zenith of superpower.

Since 1972, Watergate, the Iran hostage-taking, and the Iran-contra affair have taken their toll on the automatic political authority given the U.S. presidency by the Western democracies. The United States in becoming the world's largest debtor nation has also eroded its leadership role within the world's financial markets. The Soviet Union has similarly suffered a drop in prestige and influence. The visibly aging Brezhnev was followed in quick succession by the sickly Andropov and the wheezing Chernenko. Now we have the bustle and enthusiasm of a younger man in Gorbachev. But Soviet power, for all Gorbachev's considerable public relations talent, has fallen along with its economy. An overstretched military has been bogged down in Afghanistan for seven years. Military expenditure is absorbing too much of the Soviet Union's gross national product.

It is not just a diminution of relative economic and military power which challenges the U.S. and Soviet bipolar supremacy; their relative power position is also being eroded in the distinctive area of superpower itself, nuclear deterrence. One of the paradoxes of the nuclear arms race is that as the large nuclear arsenals in the possession of the Soviet Union and the United States built up, with each nation matching the other's every development, the very superfluousness of their arsenals for the purpose of deterrence became ever more apparent. The Chinese were the first to understand that there was a level of nuclear weaponry beyond which there was no point in continuing. China was able to assure all its strategic objectives in deterring the Soviet Union without ever conceiving of simply mirroring the Soviet nuclear arsenal. France and Britain are also discovering that same nuclear reality. When there is a 50 percent reduction in U.S. and Soviet strategic warheads, the French and British will have a more than sufficient nuclear deterrent.

All of these trends indicate that the assumption that Western Europe never should, and never would, be capable of being classified as a superpower is fast becoming out-of-date. It is time, as David Calleo argues, to use Europe's historic past as the springboard for exercising a more powerful role in building the world's common security and prosperity.

David Owen, a founder of Britain's Social Democratic Party, is a member of Parliament and a former foreign secretary.