Of all the strange bits of language to emerge from the unending war on terror, "anti-American" must count among the strangest.

It has made unwilling partisans, for and against, of an entire planet. It has conflated dissent from the foreign policy of the United States with arguments over good, evil and "the last best hope for mankind". Last - but not least - it has allowed a supremely silly view of reality to be taken seriously.

Who is authentically anti-American? All those admirers of Whitman, Twain, Dylan or Miles Davis who have no taste for vulture capitalism? Anyone who has seen the Grand Canyon or New England in the fall who is yet repulsed by drone strikes and presidential "kill lists"?

We might feel a distaste towards American exceptionalism, or religiosity, or the myths of money and democracy, yet still spend our evenings admiring the latest piece of TV dramatic art from HBO, still wondering why there is no European answer to Hollywood.

Ambivalence could be one theme, perhaps the main one, of Peter Conrad's very fine book. It has existed, in one form or another, ever since it became clear to the old world that what was emerging from a revolution against Britain in the northern Americas was without precedent. Like transatlantic trade, ambivalence has gone both ways.

All those generations of American writers who fretted over the birth of the Great American Novel were uneasily aware that their vast country lacked much of a cultural hinterland. The Europeans who sneered - who still sneer - at the crass simplicities of the American Dream yet understood that a judgement was being passed on their decadence and decay. American artists who flocked to Paris in the 1920s went because the City of Light was cheap, but also to learn what it meant to be alive. After 1945 - Conrad's point of departure - polarities were reversed.

In crude terms, the 20th century's pair of global wars settled the matter. The US emerged wealthier and vastly more powerful than before. It found a world in dire need of its billions, but also ripe for the plucking. The French understood as much almost instantly: within months of the Nazis being driven from Paris, the difference between liberation and colonisation began to seem slight.

Many American politicians could not or would not see the difference. Offered the gift of "the American way of life", indistinguishable from liberty, who could grumble? Often enough, as Conrad reminds us, the evangelism for a strange, incoherent, national ideology was explicit. The post-war Marshall Plan put a country's dollars where its mouth was. Yet the French could grumble, and still do. Much of the world, offered the leadership of a George W Bush, joins the chorus periodically when it is not enjoying the latest Hollywood blockbuster. The difference between American aid and American ownership is hard to spot.

In one sense, Conrad tells a familiar tale. Those Scots who marched in protest against the US Navy base at the Holy Loch in 1961 were big fans of American folk songs. Most of their contemporaries preferred Elvis. American literature was high on the list for any intelligent reader; the symbols of American prosperity - cars above all - had universal appeal. And when John F Kennedy was absorbed into the heart of American darkness on November 22, 1963, Scotland, like Britain, like much of the world, offered a peculiar response: we too had lost "a leader".

Simultaneously, we did not care for the idea that this distant power might well immolate the planet. Loyal Britain did not join the cousins in forging a Vietnam tragedy. The French, for long enough, would have no truck with Nato as a poor disguise for US global leadership. Elsewhere, the American habit of installing bloody dictators as bulwarks against anything smacking of Communism seemed to give the lie to all the fine talk of democracy.

Still we went on drinking the cola and watching the movies. Americans were often enough disgruntled by the fickleness of their friends in a world the US had saved from the Axis powers. It was as though the others, those Europeans in particular, felt entitled to pick and choose. A craze for fast foods was one thing. That "way of life", the flag-waving, self-regard and near-absolute lack of self-awareness? As the Americans taught us to say, we'd pass on those. We were - they said this, too - free to do so.

The story Conrad tells is one of persistent mutual misunderstanding. In the age of the internet, that is odd. Yet it can be detected still in British attitudes towards the US - generally more favourable than European attitudes - even when these are benign. Millions who are exposed to American culture in every waking hour of every day still fail to notice that the (mostly) English-speaking republic is a foreign country. Yet contemplating Britain, should the need arise, Americans are in no doubt about that.

Part of Conrad's thesis is that the era dubbed "the American century" by Henry Luce has fallen far short of 100 years. It ended on 9/11. Even the consumer bounty of the 1950s, 1960s and early 1970s, once dubbed "the Great Prosperity", is a memory. The US no longer has the economic capacity to drag a planet out of recession and depression as once it did. China, India and those other developing nations are making large claims. America's legacy is two-fold: vast military power and the conviction, uttered without irony, that Americans occupy the greatest country the world has seen.

Conrad calls it a "perpetually self-renewing place". As he makes clear, however, its citizens have not always been confident of that truth. In recent years, as the republic has settled into "culture wars" and the fixed patterns of red states and blue states, doubts over the purpose - even the meaning - of the United States have proliferated. You could see it as a sign of invincible democratic health. You could also remember that civil war has been the real state of the nation for a century and a half. What is called American self-confidence too often sounds like bluster.

Tellingly, Conrad's penultimate chapter is entitled "Why Do They Hate Us?" Baffled, the US still worries over that question. How could the last best hope be detested in an era of totalitarian states, medieval fanatics and economic decline? The author prefers to see arguments over America as "a quarrel about human possibility" in which "the removal of prohibitions and inhibitions has placed on view the best and the worst of which we are capable".

The answer to that old, romantic claim might be this: America is opposed, now and then, because of its habit of denying human possibilities which are not American. In the process, by slow yet quickening degrees, the US has exhausted its potential. The loss - as this vastly detailed and immensely subtle book shows - will be great, when it comes, but it will not be definitive. All empires claim to have achieved a kind of perfection. All empires are mistaken.