This week's ruling by the European Court of Justice, annulling an EU-US agreement on the sharing of air passenger data, is the latest hitch in a complex and often fraught relationship.
On the one hand, it is a legal technicality: the court annulled the legal basis for the agreement, not the principle of data-sharing as a counter-terrorism measure.
The European Commission is now looking at ways of keeping the substance of the deal but shifting to a new legal basis.
On the other, it is an indication of one of the most important differences between the two sides of the Atlantic.
The US regards itself as being at war: that justifies extraordinary measures. The EU, broadly speaking, regards terrorism as a continuing threat, but not a war as such.
Critics of the court's ruling say it will cause chaos for travellers if a new agreement is not concluded by the court's deadline of 30 September 2006. The American requirement for passenger data remains.
The only difference, the critics say, is that passengers could have to queue for hours at either end to provide the information the US is entitled to require of people entering its territory.
Civil liberties
The leader of the UK Conservatives in the parliament, Timothy Kirkhope, said the ruling would place a strain on the EU-US relationship.
"The US will be tougher in its requirements (for data) because of the hostility of the European Parliament to the United States," said Mr Kirkhope, who is also the Conservatives' justice and home affairs spokesman in Brussels.
"Guantanamo Bay is an anomaly. The United States must take measures to close the camp as soon as possible"
The legal challenge to the EU-US agreement came from the European Parliament. A majority of MEPs were concerned that the deal infringed the civil liberties of EU passengers.
The chairman of the parliament's civil liberties committee, French MEP Jean-Marie Cavada, said it was "regrettable" that the court ruled only on the technical framework, not on what he called a "violation of fundamental rights".
UK Labour MEP Arlene McCarthy, whose constituency includes Manchester airport, said she was not sure the amount of data the US was demanding was really required for security purposes. But she urged the EU to find a pragmatic solution.
"Do I really want to ask my constituents to stand in line for three hours (when they're travelling to the United States)?" she said.
Prison 'irritant'
Another point of friction in what the US calls the "war on terror" is the detention camp at Guantanamo Bay in Cuba. The US says the detainees are "illegal combatants," not prisoners of war under the Geneva Conventions.
EU governments disagree. Speaking in the European Parliament on Wednesday, Austrian Foreign Minister Ursula Plassnik, whose country holds the EU presidency, said the EU had raised the issue with Washington many times.
"Guantanamo Bay is an anomaly," she said. "The United States must take measures to close the camp as soon as possible."
The issue is likely to be raised at the EU-US summit in Vienna on 21 June.
Arlene McCarthy, who was part of a European parliamentary delegation to Guantanamo last month, said the camp showed the US was taking a "unilateral approach" to counter-terrorism.
The camp had changed since it opened in 2001, Ms McCarthy acknowledged. Medical facilities for detainees were better than those available to homeless Americans in Washington, she said.
"But that misses the point," she argued. The fact that more than 400 people remain imprisoned without trial at Guantanamo Bay had been an "irritant" for the EU for some time, she said.
A committee of MEPs is also investigating whether some of the detainees at Guantanamo and other US interrogation centres were illegally transported and detained by the CIA on European territory.
In its interim report in April, the committee said it had evidence that the CIA had operated more than 1,000 secret flights over Europe.
Iran challenge
John Bellinger, the legal adviser to US Secretary of State Condoleezza Rice, said there had been CIA flights, but most were carrying experts or forensic evidence. Only a handful had carried terrorism suspects.
Timothy Kirkhope said the committee was led by "people hostile to the United States". Certain political groups in the parliament had, he said, "anti-American views... some based on distrust going back many years".
In other areas, though, there is more co-operation. The EU and the US both cut off funds to the Palestinian Authority after the militant movement Hamas won parliamentary elections in January. They are now working together on ways to channel funds to the Palestinians while bypassing Hamas.
And on the sensitive topic of Iran's nuclear ambitions, the US has now announced it will join multilateral talks with the EU-3 - France, Germany and Britain - as well as Russia and China.
While the US was pursuing a tough line with Iran, the EU-3 wanted negotiations to continue.
"Direct US participation would be the strongest and most positive signal of our common wish to reach an agreement with Iran," said EU foreign policy Javier Solana in a statement.
The US is attaching conditions: it still insists that Iran must suspend uranium enrichment. But for the EU, it is a vindication of a multilateral approach, and a far cry from the dark days of 2003, when the Iraq war threatened to drive an irreparable rift between old allies.
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