George Bush begins his first trip to Europe tomorrow, a visit that is being billed as long on charm, short on specifics for the new US President. Mr Bush has much bridge-building to do with a European audience sceptical of both his foreign policy credentials and worried about what is perceived as the increasing US tendency to go it alone.
Mr Bush's busy five-day visit starts in Spain, continues in Brussels, with meetings at headquarters of the North Atlantic Treaty Organisation, and with the Belgians. He then flies on to Sweden where he meets European Union leaders in three sessions of talks, meets the Swedes separately, and then on to Poland, and finally to Slovenia for a meeting with the government there and a summit with Russia's President Putin.
US officials and the President's National Security Adviser, Dr Condoleezza Rice, are upbeat, emphasising that what disagreements there are at the margins of an enormously strong relationship. And they talk enthusiastically of the yearly $3 trillion in mutual trade and investment.
"This is a relationship under some stress but by no means in crisis," the director of policy and planning in the State Department, Dr Richard Haas, insists.
But others, like Dr Ivo Daalder, a former National Security Council director of European Affairs, argue that the normal turbulence that characterises the margins of a complex relationship actually conceals a more significant long-term estrangement between the EU and the US attributable to the structural changes in the world since the end of the Cold War. Not so much a divorce as the growing apart of a couple whose children have left home and find they have less in common than they thought.
The unifying threat of the Cold War is no more and the US has emerged as uniquely powerful, the global power. Europe has become increasingly preoccupied with its own internal construction and managing the transition of former communist regimes. Dr Daalder sums it up as "the EU is worried about failed states, the US, about rogue states".
Such changes in the underlying strategic reality have both turned the US's attention to Asia as its major preoccupation and reinforced its tendency to unilateralism - by definition involvement as one of many in multilateral organisations like the UN undermines hyper-power status.
Such changes play to the grain of Mr Bush's political instincts despite his election pledge to promote a "humble" foreign policy. He acknowledges that the Europeans see him as isolationist and promises that: "I'll ease their concerns. We're an internationalist government."
He has a job on his hands, not helped by the signal sent last week when the US told the Europeans that they want to halve the number of EU-US summits to one a year. The Administration has learnt from its early, ham-fisted repudiation of the Kyoto climate change protocol that its European friends must not be taken for granted, as Dr Rice admitted last week to journalists.
But a willingness to discuss its missile defence plans with NATO partners, Russia and China, although welcome, should not be confused with a willingness to listen.
Dr Philip Gordon, also a former member of the NSC staff, warns of the danger of an international Jeffords effect - the senator who defected to the Democrats was taken for granted by a White House which talked about listening and bipartisanship but was unable to convince it really meant it.
The European response to the missile project has been muted, a fact the White House makes much of, but that is largely because the US has refused to elaborate which of many alternative forms of missile defence it prefers. It is not just a European reluctance to embrace "new strategic challenges." Most EU states do not share US paranoia about "rogue" states and see security in a substantially different way as largely a political, rather than hardware, problem.
Neither side expects Mr Bush to detail his missile plans this trip but he will come under pressure to come up with a coherent alternative approach to Kyoto on global warming. The issue is being discussed by a high-level cabinet working group which has yet to reach definitive conclusions but the publication last week of a scientific report strongly linking global warming to human activities has made Mr Bush's task more difficult.
Several EU leaders are certain to want to have a go at him on the issue for domestic reasons and repetition by him of a voluntarist approach to fuel targets and of the US insistence that the developing world must also share the burden of cuts will not go down well.
EU diplomats hope that a more positive tone to the talks can be achieved if Mr Bush is willing to give a strong endorsement of European plans for the Rapid Reaction Force to which the US is now more solidly committed following a recent tentative agreement with Turkey on its relationship to the force.
They hope that in the discussion on the Balkans he can allay fears that the US wants to pull its troops out and will be willing explicitly to endorse the comments of the Secretary of State, Mr Colin Powell, who pledged that "we went in together and will leave together".
NATO discussions will also focus on enlargement, with the US determined that next year's summit should bring in more of the eastern Europeans. It would even like to name candidates now.
A number of trade issues may also add to the friction of this week's meetings. Both sides would like to help kick-start another world trade round at November's Qatar summit, but the much more restrictive US agenda has made a common approach even on a launch of the process difficult to achieve. A joint statement of substance out of Gothenburg would be seen as a real achievement.
Bilateral trade issues, such as recent US threats to steel imports and the $4 billion row about "foreign sales corporations", are also still major irritants. If Mr Bush wants to convince that he is genuinely committed to multilateral trade regulation, he will be told, then he must act to implement WTO rules in both cases to prevent serious escalation of the disputes.
The EU summit will also see an important discussion of the prospects for a global fight against communicable diseases, most notably AIDS. Although both sides are committed to the global trust fund, they have differences over whether the pharmaceutical companies should be required to back tiered pricing in the developing world and whether the international community should define the right to treatment as a basic human right.
Mr Bush has a lot of convincing to do and his Texan smile may just not be enough.