President Bush and Russian President Vladimir Putin have ended their Texas summit with promises of cooperation, and a pledge to keep working on the thorny issue of missile defense. Before the Russian leader left Texas, both men made a joint appearance at a high school near the Bush ranch.

It was a lesson in foreign relations that the students at Crawford High School will never forget. "I bet a lot of folks here, particularly the older folks, never dreamt that an American President would be bringing the Russian President to Crawford, Texas," he said. George W. Bush and Vladimir Putin, dressed in casual garb and trading jokes, stood side-by side in the high school gymnasium. The mood was light-hearted, despite the weighty issues discussed during their summit.

They joked with the students like two old friends, friends who quarrel sometimes, but are comfortable together.

President Bush talked about their conversations over meals of Texas barbecue and pecan pie. He marveled over the way the world has changed since the days of the Cold War.

"When I was in high school, Russia was an enemy. Now, the high school students can know Russia as a friend; that we are working together to break the old ties, to establish a new spirit of cooperation and trust so that we can work together to make the world more peaceful."

During their three days of talks, first at the White House and then at the Bush ranch, the two leaders focused on Afghanistan and arms control. They agreed to deep cuts in long-range nuclear warheads. But they did not reach a deal on how to pave the way for testing and deployment of a U.S. missile defense shield.

They seemed a bit startled when, during a question and answer session, one of the high school students asked about the missile defense program. "I was wondering if you've come to a conclusion about whether or not to deploy a national missile defense system?," he asked. Mr. Bush replied, "Are you with the national press corps?"

But President Bush quickly turned serious. He returned to a theme that has echoed throughout this summit: That U.S.-Russian ties have entered a new phase and arms control is no longer the driving force. "We've found many areas in which we can cooperate and we've found some areas where we disagree. But nevertheless, our disagreements will not divide us, as nations that need to combine to make the world more peaceful and prosperous," he said.

At issue is the fate of the Anti-Ballistic Missile Treaty, which bars testing and deployment of a missile shield. President Putin said they would keep talking. "He said both the United States and Russia want to achieve national security and guard against future threats. He said there is enough common ground to enable the two countries to eventually come up with a solution acceptable to all," the Russian leader said.

The two Presidents took questions from the students for about 40 minutes. When asked about a reciprocal trip to Russia, President Bush said he would like to go sometime in the new year. He said he wants to visit both Moscow and St. Petersburg, Vladimir Putin's home town. But when President Putin jokingly offered winter in Siberia, Mr. Bush responded with an invitation for a return visit to Texas in the sweltering heat of summer.