BRUSSELS (Reuters) - Muammar Gaddafi's death will probably bring a swift conclusion to NATO's mission in Libya, offering a moment of relief and satisfaction after a seven-month campaign that exposed strains and doubts within the alliance.

French President Nicolas Sarkozy said on Friday that the NATO operation was coming to an end, while ambassadors of the alliance are expected to decide in Brussels later in the day to finish a mission which NATO took over on March 31.

Officials and diplomats said the air and sea campaign was likely to be wound down over the next two weeks. But NATO has already hailed a successful implementation of its U.N.-mandated mission to protect Libyan civilians during the uprising against Gaddafi, who was killed on Thursday.

It can point to some big positives -- not least that it did not suffer a single casualty, despite flying 26,000 air sorties, and kept unintended civilian casualties to a minimum thanks to the use of precision-guided munitions.

However, the campaign exposed divisions. Some leading NATO members including Germany questioned the intervention's wisdom and only eight of the 28 member states took part in strike missions. It also drew criticism from countries such as Russia which accused NATO of overstepping its United Nations mandate.

Doubts grew as the campaign dragged on longer than expected at a time when defense budgets were being slashed due to the West's worst financial crisis since the 1930s. European allies drew sharp rebukes from the United States for failing to invest sufficiently in essential equipment.

Francois Heisbourg, chairman of the International Institute for Strategic Studies think tank, said the operation would and could be declared a success for the West -- particularly by Britain and France, which carried out the bulk of combat missions. But it could not have succeeded without strong U.S. support, despite an attempt by President Barack Obama to make sure the United States took a back seat in the conflict.

While the United States stepped back from a leading role in combat missions after the initial phase of Western bombing, it provided the bulk of vital intelligence and logistical support including air-to-air refueling.

"It's obviously a success for the British and the French, without whom none of this would have happened," Heisbourg said. "And it can be counted as a success for the coalition operating under the NATO label, largely with American means, so it's obviously a U.S. success as well."

Defense CUTS STRAINED MISSION

However, the mission has also been embarrassing for Britain which was shown to be overstretched after entering a new war just after announcing punishing defense budget cuts.

"Because most of the munitions used by the French were French-produced, they had no basic problems of supply. The Brits had a rougher time for several reasons as they are quite heavily reliant on American-made munitions," Heisbourg said.

"And because it is not the American way to provide stockpiles but to deliver munitions on an as-you-go basis, the British very rapidly ran out of some of the more basic munitions and had to go like Oliver Twist to the Americans and ask for more -- something the Americans chose to make public."

Any NATO euphoria from an end to the Libyan operation is likely be short-lived as this will throw the focus back onto its troubled mission in Afghanistan.

"Libya for the alliance was a rather welcome moment as it made everybody forget about Afghanistan for a few brief months," Heisbourg said.

"Now, once again NATO is going to be exposed to the Afghan dossier and that's not in great shape, to put it mildly," he said. "Libya means success and Afghanistan means trouble."

Daniel Keohane, of the EU Institute for Security Studies, said the end of the mission would be particularly welcome for Sarkozy and British Prime Minister David Cameron. Both had appeared exposed as what optimists had forecast would be a brief campaign dragged over the summer.

"I suspect they will at first be quite relieved," he said, adding that both Sarkozy and Obama would be glad too not to have Libya hanging over their presidential election campaigns next year and to able to point to a successful mission.

Whether NATO leaders would be able to make such claims for long remains unclear, though. There are concerns about divisions and radicalism in the forces that toppled Gaddafi, and Western capitals are alarmed about large numbers of missing portable anti-aircraft missiles which officials fear could be used to threaten civil aviation.

NATO Secretary-General Anders Fogh Rasmussen alluded to future problems on Thursday when he called on Libyans to put aside differences and work together, urging the transitional administration to avoid reprisals against Gaddafi supporters.

"It's still not clear who the rebels are and while it may be the end of the war, it's only the beginning of the transition," Keohane said. "So much depends on how the rebels manage the situation on the ground and the question is: do we know who these people are?

"And as to calling it a success, it depends on your starting point. If the question was to get Gaddafi and protect civilians, well yes, but we don't know if Libya will become a democracy.

"In one sense, this is a big tactical success, but the big strategic question is: Will Libya become a democracy? And that's still not clear."

(Reporting by David Brunnstrom)