Nato's new role in charge of the International Security Assistance Force (Isaf) in Afghanistan is the alliance's first major operation outside Europe.
It took command from Germany and the Netherlands, which have led the force jointly since February.
Kabul is Nato's first major assignment outside Europe
But the alliance has taken over indefinitely, removing the need to find a new lead nation every six months.
Nato spokesman Mark Laity says this will ensure greater continuity, enabling Isaf to take a longer-term view of Kabul's security problems.
The force has some 5,000 soldiers from 31 countries - with most of the troops coming from Nato states.
Under its United Nations mandate, the security force is responsible only for the capital and the surrounding area.
There have been constant demands for Isaf to extend its area of operations throughout Afghanistan.
The Nato spokesman says it is too early to discuss any changes to Isaf's area of operations.
But German Defence Minister Peter Struck has called for international troops to be deployed beyond Kabul once his country hands over control to Nato.
Helping Afghanistan is an appropriate task, Nato says
He said Germany was considering deploying peacekeepers in the northern town of Kunduz.
Such a deployment would probably be part of what are known as Provincial Reconstruction Teams - groups of up to 100 military personnel deployed to regional centres to help provide security for aid and reconstruction work.
Four such teams are already operating in various provincial towns. They come under the command of the American-led coalition, not under Isaf.
For the Nato alliance itself, involvement in Afghanistan is the first major step in its adaptation to the post-Cold War world.
The collapse of the Soviet bloc left the alliance looking for a purpose. The attacks against the United States on 11 September 2001 provided that purpose.
At the Nato summit in Prague last year, the alliance's leaders agreed that the old system of concentrating on defence of geographical borders was no longer sufficient.
In a world of globalised threats from terrorism, Nato officials now say the alliance must act to counter those threats wherever it sees them.
Helping to prevent Afghanistan from collapsing into a failed state is therefore an appropriate task for the new Nato.
It is perhaps too early to ask whether Afghanistan will provide lessons that could be applied elsewhere.
But already the German defence minister has suggested to a German newspaper that German troops could take part in a Nato force in Iraq if there were a UN mandate.
Nato forces are already involved in peacekeeping missions in Bosnia and Kosovo.
The logistics of deploying in the Balkans are much less challenging than in Afghanistan, as the region is closer to home and infrastructure is more developed.
In remote, impoverished, landlocked Afghanistan all equipment and supplies have to be brought into the country, usually by air.
The Kabul area of operations is much smaller that in the Balkans, but Afghanistan will provide many challenges with its ethnic divisions and conservative tribal culture, and the ever-present threat from Islamic extremists.