LONDON - The man picked to be U.S. President Barack Obama's top military adviser said Wednesday that the United States does not yet understand the long-term implications of Osama bin Laden's death.

Gen. Martin Dempsey, the current U.S. Army chief of staff, told a military think tank in London that military leaders are still gauging the likely impact on al Qaeda's capability and future threat.

Bin Laden's killing last month was "a great moment in terms of taking the leadership of al Qaeda and creating difficulties for that organization," Dempsey told Britain's Royal United Services Institute.

But Dempsey said that he and others haven't "yet come to understand what his particular demise might mean, and might mean for the future."

Obama has announced Dempsey as his pick to succeed Adm. Mike Mullen as the Joint Chiefs of Staff chairman. The nomination of the 59-year-old seals Obama's overhaul of his military and intelligence leadership.

Dempsey told an audience of military leaders from the U.S., Britain, China and Brazil that it also is not yet clear how the Arab revolts across the Middle East and North Africa will shape relations across the wider world.

"I think our imaginations are just beginning to touch the edges of what that might mean," he said, "how that will affect the global commons, not just the narrow Middle East itself."

He said one lesson for military leaders was to shape their forces to be ready to adapt to fast-changing events -- developments which may not reflect recent global history.

Speaking of former Egyptian President Hosni Mubarak, Dempsey said: "What brought down Mubarak was Facebook and social networking, a leaderless organization that rose up and we call the Arab Spring. So things can happen much more quickly than in the past."

A veteran of two wars with Iraq, Dempsey hailed the increasing capability of that nation's army and police, but acknowledged the U.S. and its allies face a tougher task in training local security forces in Afghanistan.

In Afghanistan, the "challenge has been, and continues to be, different," he said.

"There has been enormous progress at a tactical level, but that progress has been harder to link together -- to knit together -- at a national level," Dempsey said.

The four-star general did not offer any comment on his nomination as the next chairman of the Joint Chiefs of Staff, and declined to answer reporters' questions on the issue.

Gen. Peter Wall, head of the British army, told the conference the international deadline of 2014 to withdraw foreign combat troops from Afghanistan is helping to focus attention on developing a political solution to the country's insurgency.

"Key to terminating any insurgency is going to be the form of political resolution, something over which we as a nation, and certainly we as an army, do not have direct control. This is very much an issue for Afghan people, Afghan politicians and those in the region," Wall said.