By John Leyne BBC Washington correspondent

One of the world's key strategic alliances - that between Saudi Arabia and the United States - has been in deep trouble since the attacks on 11 September.

While Americans are angry that most of the hijackers were Saudis, the Saudi Government keeps pressing for more involvement by the US in ending the conflict between the Palestinians and Israelis.

George Bush offered a friendly welcome to Prince Abdullah

As a result, there is growing pressure from many US lawmakers for a fundamental reassessment of the relationship.

Speaking at a recent Congressional hearing, one contributor pointed out that Saudi Arabia has one of the worst records in the world with regard to human rights.

The Gulf War

It is now 12 years since American troops were sent to the Gulf following Iraq's invasion of Kuwait.

Democratic Congressman Tom Lantos is one of many on the Hill increasingly bitter that the Saudis are not more grateful for America's protection:

"The United States saved the House of Saud. Had we not done so, the House of Saud today would be a villa on the French Riviera rather than an important country in the region," he said.

In a long litany of complaints against the Saudis, Mr Lantos headlines their treatment of women.

He recalls an anecdote about the recent visit of the Saudi Crown Prince to President Bush's ranch in Texas: "During his recent visit, the Crown Prince, approaching his landing target in Texas, apparently had the plane call for a male air traffic controller to guide the plane down," he said.

Mr Lantos believes that Saudi Arabia is ungrateful for US support

President Bush himself went out of his way to offer a friendly Texas greeting to Crown Prince Abdullah.

But the rest of America cannot get over the prominent role of Saudis in the 11 September hijackings.

Right-wingers in Washington - and they are very influential in this administration - want things to change.

William Kristol, editor of the magazine The Weekly Standard, is one such right-winger. He says the US needs to rethink its relationship with Riyadh.

"For we are now at war - a war with terror and a war with terror's main sponsor in the world, radical Islam," he says.

"And in this war the Saudi regime is more part of the problem than part of the solution."

James Wolsey has called for more co-operation with Russia

The former CIA director, James Wolsey, even argues for America to work for more fuel efficient cars in order to reduce dependence on Saudi oil - and that is almost a sacrilege on the right of American politics.

Mr Wolsey calls for helping the Russians to produce more oil and for gradually pulling out of Saudi military bases.

"As a general matter, I believe these three steps or steps like them, taken toward reducing our reliance on the Saudis, reducing our reliance on their bases, reducing our reliance on their oil, are very much in the security interests of the United States."

Future relationship

So what does this all amount to? Already the American military is reducing its reliance on key Saudi air bases.

But stopping that thirst for Saudi oil - that is a much tougher call.

Judith Kipper, a prominent Middle East analyst in Washington, believes there is no chance of a break in relations between Saudi Arabia and the US.

"The US understands perfectly well that the US/Saudi strategic relationship is a vital interest of the United States," she says. "It serves American interests and is a relationship that has been sustained through many crises and will be sustained for the foreseeable future."

But this could still be the beginning of a long, slow process of these two strangest of allies gradually drawing apart.