MADRID, Spain – The electoral rebuke for President Bush and the resignation of his defense secretary, both deeply unpopular away from American shores over the Iraq war, was celebrated throughout Europe, the Middle East and Asia.

Still, there was concern Wednesday that a Washington power split and a severely weakened Bush might mean uncertainty in crucial areas like global trade talks.

On Iraq, some worried that Democrats will force a too-rapid retreat, leaving the country and the region in chaos. Others said they doubted the congressional turnover would have a dramatic impact on Iraq policy any time soon, largely because the Democrats have yet to define the course they want to take.

But from Paris to Pakistan, politicians, analysts and ordinary citizens said Wednesday they hoped the Democratic takeover of at least one house of Congress would force Bush to adopt a more conciliatory approach to global crises, and teach a president many see as a “cowboy” a lesson in humility.

In an extraordinary joint statement, more than 200 Socialist members of the European Parliament said the American election results were “the beginning of the end of a six-year nightmare for the world.”

Defense Secretary Donald H. Rumsfeld was both deeply hated and grudgingly admired overseas as a key architect of the wars in Afghanistan and Iraq.

The Afghan government expressed sadness over Rumsfeld’s abrupt departure, with Jawed Ludin, the chief of staff for Afghan President Hamid Karzai, saying the country was “very pleased and very grateful for (Rumsfeld’s) support for Afghanistan.”

But Venezuelan President Hugo Chavez, who has railed against the Bush administration, was gleeful.

“Heads are beginning to roll,” Chavez said. “It was about time for him to resign. The president should resign now.”

In Paris, American expatriates and French citizens alike packed the city’s main American haunts to watch results overnight and early Wednesday, with some standing to cheer or boo as vote tabulations came in.

One Frenchman, 53-year-old teacher Jean-Pierre Charpemtrat, said it was about time U.S. voters figured out what much of the rest of the world already knew.

“Americans are realizing that you can’t found the politics of a country on patriotic passion and reflexes,” he said. “You can’t fool everybody all the time _ and I think that’s what Bush and his administration are learning today.”

Bush is deeply unpopular in many countries, with particularly intense opposition to the war in Iraq, the U.S. terror holding facility at Guantanamo Bay, Cuba, and allegations of Washington-sanctioned interrogation methods that some equate with torture.

Many said they thought the big gains by Democrats signaled the beginning of the end of Bush’s tenure.

In Copenhagen, Denmark, Jens Langfeldt, 35, said he didn’t know much about the midterm elections but was opposed to Bush, referring to the president as “that cowboy.”

In Sri Lanka, some said they hoped the rebuke would force Bush to abandon a unilateral approach to global issues.

“The Americans have made it clear that current American policy should change in dealing with the world, from a confrontational approach, to a more consensus-based and bridge-building approach,” said Jehan Perera, a political analyst.

The Democratic win means “there will be more control and restraint” over U.S. foreign policy.

Passions were even higher in Pakistan, where Bush is deeply unpopular despite billions in aid and support for President Gen. Pervez Musharraf.

One opposition lawmaker, Hafiz Hussain Ahmed, said he welcomed the election result, but was hoping for more.

Bush “deserves to be removed, put on trial and given a Saddam-like death sentence,” he said.

But while the result clearly produced more jubilation than jitters, there were also some deep concerns.

In Denmark, Prime Minister Anders Fogh Rasmussen told broadcaster TV2 he hoped the president and the new Congress would find “common ground on questions about Iraq and Afghanistan.”

“The world needs a vigorous U.S.A.,” Fogh Rasmussen said.

There was also some concern that Democrats, who have a reputation for being more protective of U.S. jobs going overseas, will make it harder to achieve a global free trade accord. And in China, some feared the resurgence of the Democrats would increase tension over human rights and trade and labor issues. China’s surging economy has a massive trade surplus with the United States.

“The Democratic Party … will protect the interests of small and medium American enterprises and labor and that could produce an impact on China-U.S. trade relations,” Zhang Guoqing of the state-run Chinese Academy of Social Sciences said in a report on Sina.com, one of China’s most popular Internet portals.

The prospect of a sudden change in American foreign policy could also be troubling to U.S. allies such as Britain, Japan and Australia, which have thrown their support behind the U.S.-led invasion of Iraq.

“The problem for Arabs now is, an American withdrawal (from Iraq) could be a security disaster for the entire region,” said Mustafa Alani, an Iraqi analyst for the Gulf Research Center in Dubai. He said the Middle East could be left to cope with a disintegrating Iraq mired in civil war, with refugees fleeing a failed state that could become an incubator for terrorism.

It was unclear, however, whether the American election would bring a major shift in Iraq, in part because the Democrats have not come ahead with a clear action plan, said Michael McKinley, a political science professor at the Australian National University.

“There would have been some concern in policy making circles here if the Democrats had said, ‘We are definitely going to withdraw by Christmas,'” McKinley said. “But they’re not able to say that.”