President Bush is in St. Petersburg, the hometown of Russian President Vladimir Putin. During a joint appearance at a local university, Mr. Bush said he is optimistic about Russia's future.

It was a wide-ranging discussion, involving two presidents and a huge auditorium packed with university students and faculty.

One day after they signed a landmark arms reduction treaty in Moscow, Presidents Bush and Putin stressed that relations between their two countries have entered a new phase. Both said they were pleased with the results of their summit.

President Bush put it this way, "The treaty we signed says a lot about nuclear arms. It speaks about the need for peace. But it also says the Cold War is over, and America and Russia need to be, and will be, friends for the good of the world," he said.

The two presidents seemed very much at ease, calling each other "George" and "Vladimir," and occasionally joking with the audience. The questions dealt with many facets of U.S.-Russia relations - from trade to the personal ties between the two leaders.

No one asked about arms control, another sign of change in the post Cold War world. Instead, questioners wanted to know about Russia's bid to join the World Trade Organization, and if this new warm relationship is permanent.

President Bush said he backs Russian entry into the WTO, if certain conditions are met. President Putin responded with a smile. "..and he said that he is for it. If that's sufficient, I'm in. But on conditions acceptable to Russia," he said laughing.

They turned serious when talking about their individual leadership styles and their hopes for the future. Mr. Bush said he is optimistic about Russia. "A strong and prosperous and peaceful Russia is good for America," Mr. Bush said.

It was a repeat performance for the two presidents. Last November, during President Putin's trip to the United States, they appeared together at a high school near the Bush family ranch in Texas. The event was so successful, they decided to do it again - with a slightly older audience - at the university where Vladimir Putin once studied law.