By Belinda Rhodes BBC Correspondent

Last week in Afghanistan several American soldiers lost their lives in ferocious fighting with al-Qaeda and Taleban forces - a shock to anyone who had hoped that Osama Bin Laden's terrorist network had breathed its last.

US Defence Secretary Donald Rumsfeld is one of those warning against assuming the danger of al-Qaeda mounting attacks elsewhere has gone.

They're determined, they're dangerous, they will not give up without a fight

US Defence Secretary Donald Rumsfeld

"We've made very good progress but, as I've said repeatedly, the task is far from over," he said after the battles in eastern Afghanistan.

"Not all Taleban and al-Qaeda forces have been defeated, substantial pockets of resistance remain.

Mr Rumsfeld said militants were hiding in villages and mountains along Afghanistan's borders and were waiting for opportunities to continue their fight against the West.

Strong bases

Certainly in Afghanistan, al-Qaeda still has the power to wreak havoc.

Osama bin Laden has yet to be caught, dead or alive

And, as far as we can tell, Osama bin Laden is still at large.

But based on what is known about the nature of al-Qaeda, many observers say the death or capture of its leader is immaterial.

Abdel Bari Atwan, editor of the London-based Al Quds newspaper, says the organisation would continue its activities without Bin Laden.

"Al-Qaeda is not really a one-man show," he said.

"Definitely it is more than that because it is based on many strong bases, and the strongest of them is the Islamic faith - radical interpretation of Islamic Jihad.

The tremendous number of arrests... certainly foiled some planned further terrorist attacks

Terrorism expert Dr Magnus Ranstorp

"Second thing, it is actually based on hatred toward the United States and its foreign policies.

"So if Osama bin Laden is killed or captured, I don't think al-Qaeda will finish."

But despite the recent battles with al-Qaeda and the failure to kill or capture its leader, there is evidence that the group's activities beyond Afghanistan's borders have been significantly disrupted.

US embassies targeted

Dr Magnus Ranstorp, a terrorism expert at the University of St Andrews, said offences had been prevented in the US and Europe.

"I think the tremendous number of arrests that were made in the United States certainly foiled some planned further terrorist attacks in the US," he said.

The post-11 September crackdown prevented other attacks, experts say

"Of course, in Europe there has been tremendous law enforcement success in actually foiling a whole range of terrorist activity, ranging from plans to attack Nato headquarters [to] the European parliament.

"There've been three serious plans to target the US embassies in Paris and in Rome."

Huge challenge

The range of targets meant there had to be a global coalition against al-Qaeda and results would not necessarily come quickly, Dr Ranstorp said.

"It's going to be a long law enforcement effort, let alone trying to bring them to justice, and in really making a serious dent in this organisation," he said.

Even before the US-led military campaign in Afghanistan, many al-Qaeda members were based elsewhere - in Europe, the Middle East and in the US.

There's nothing that we would think of as a well-organised military command structure

Washington journalist Edward Alden

And many of those who were operating from Afghanistan left before the Americans arrived, predicting a strong response to 11 September.

Scattered all over the globe, they present a huge challenge to those trying to catch them.

But as Edward Alden, Washington correspondent for the Financial Times, points out, the loss of the Afghan headquarters was a blow to al-Qaeda.

E-mails sent

"There's no question that contact between whatever remains of the central leadership in Afghanistan and the rest of al-Qaeda's network around the world has been significantly disrupted," he said.

There was some evidence from areas such as Pakistan that al-Qaeda members were exchanging e-mails from internet cafes in attempts to rebuild communication links, Mr Alden said.

"But there's certainly nothing that we would think of as a kind of well-organised military command structure."

There is little evidence as yet that al-Qaeda plans to regroup in one particular place, rather than continue to operate from many different countries.

But there is plenty to show that, even as a diffuse grouping driven more by conviction than leadership, it stills poses a significant threat.