WASHINGTON -- Winding down his presidency, George W. Bush is beginning his farewell tour on the world stage trailed by questions about how much clout he still wields.

Unpopular abroad, as he is at home, Bush nevertheless has been a commanding presence among world leaders for the past seven years. Now, with fewer than 300 days left in his term, other presidents and prime ministers are looking beyond Bush to see who will occupy his chair a year from now.

It is an open question whether Bush's foreign policy priorities will be embraced by his successor in the White House. Other world leaders have to calculate how far they should step out on the ledge with a president whose days are numbered and whose legacy had been darkened by the long and costly war in Iraq.

Air Force One will roar out of Andrews Air Force Base on Monday to whisk Bush to the first in a long-planned series of global goodbye events. After a brief stop in Ukraine, Bush stops in Romania to attend his last summit with NATO leaders.

A few days later, Bush will land in the Black Sea resort city of Sochi for his probable final meeting with Vladimir Putin as Russian president; his successor takes over in May.

Relations between Washington and Moscow have plummeted in recent years amid a welter of bitter disputes, and the talks in Sochi have raised hopes that Bush and Putin can lay the foundation for repairing ties.

This is the busiest travel year in Bush's presidency in terms of the sheer number of trips.

He went to the Middle East in January and to Africa in February. After he returns from NATO and Russia, he has five more major excursions on the books -- from Europe to Asia, the Middle East to South America.

In June, he will travel to Slovenia for his final summit with the European Union.

He will attend his last summit of Group of Eight leaders in Japan in July. He will go to Peru in November for his final meeting with Pacific Rim leaders at the Asia-Pacific Economic Cooperation forum.

More trips may be added as Bush moves closer to the exit and his successor emerges.

Around the world, there are hopes the next president will adopt a different style from what critics have called Bush's cowboy diplomacy and go-it-alone foreign policy.

"There seems to be a great deal of enthusiasm, particularly for [Barack] Obama but also Hillary [Clinton] on the other side of the Atlantic, that there's going to be some revitalization of the trans-Atlantic partnership and we start with a clean slate and a new chapter and all the rest," said Julianne Smith, Europe program director for the Washington-based Center for Strategic and International Studies.

"I think a lot of these European countries have found a way to get past the dark shadows of 2003 and '04 when we had divides over Iraq and all the rest," she said. "And many of them are looking forward now to the next president in Washington and are already thinking about what the 2009 [NATO] summit will bring."

A change of leaders in Germany and France -- which led the opposition to the war in Iraq -- helped improve sour relations between Europe and the United States. But there still is some lingering ill will. There has been much trans-Atlantic bickering and finger-pointing, most notably about the purpose of NATO and its commitment to Afghanistan.

The United States has criticized Germany and other European allies that have refused to allow their troops in Afghanistan to be deployed to the southern heartland of the Taliban insurgency alongside United States, British, Canadian, Dutch and other contingents. Defense Secretary Robert Gates has proclaimed himself "a nag on the issue."

European leaders have expressed skepticism about winning the Afghanistan mission on the ground or that NATO has the capabilities it needs to succeed. Moreover, they face public opposition about the war and pressure for an exit strategy.

Europeans also say the United States has been too preoccupied with Iraq and has not put the proper focus or devoted enough political capital on Afghanistan.

"Europeans are often quick to dismiss the Afghan mission as an unnecessary part of President Bush's war on terror," said Philip Gordon, a former director for European Affairs at the National Security Council and now a senior fellow at the Brookings Institution.

"But I believe they can be persuaded that the mission is actually in Europe's own strategic and humanitarian interest," he said.

Some of the differences appear to be narrowing. French President Nicolas Sarkozy has pledged to deploy more troops to fight the Taliban if Afghans also get more responsibility and there is better coordination of nonmilitary efforts.

Bush, in a pre-trip interview, said it would be hard for any nation to trump Britain as "our greatest ally" -- particularly given its strong backing in Iraq.

But Bush said the relationship with France "is changing for the better and President Sarkozy gets a lot of credit for that."

Sarkozy's promise of more French troops in Afghanistan "will pretty much ensure that this [NATO] conference is a successful conference," the president said.