Despite complaints that George W. Bush has ignored Russia during his presidency, one fact cannot be disputed: In visits, he has made President Vladimir Putin a priority.

Bush has held more one-on-one meetings with Putin than with any other world leader, with the exception of Britain's Tony Blair.

Now, with their 28th and presumably final visit looming, the two presidents appear hard-pressed to show that the previous meetings have meant something.

"These guys are playing for history," said Andrew Kuchins, head of the Russia program at the Center for Strategic and International Studies.

Bush and Putin will huddle for talks Sunday at Putin's Black Sea villa in sun-drenched Sochi. The presidents hope to thrash out an agreement that spells out their achievements and provides a road map for their successors to follow.

If they fashion a deal, it would be a something of a first. In the twilight of their terms in office, Bush and Putin seem to realize that they have spent years talking up their personal friendship but agreeing on little of substance. In fact, they have all but dismantled the system of control over nuclear and conventional weapons.

"The presidents' friendship is a good thing but only if it has been reinforced by some legally binding bilateral agreements," said Vagif Guseinov, director of the Moscow-based Institute of Strategic Studies and Analysis. "Unfortunately, not one such agreement has been signed in the past eight years."

The sole exception, arguably, was the Moscow Treaty, a 2002 pact that calls for Russia and the United States to cut their strategic nuclear arsenals by about two-thirds by 2012, when it expires. But critics like Guseinov said the treaty was "fuzzy" and its implementation has been hard to control.

Another key arms agreement, the Strategic Arms Reduction Treaty, or START, is due to expire next year, and U.S. and Russian officials have not agreed on a successor pact.

Other treaties have been ditched or are headed toward collapse. In 2002, the United States unilaterally withdrew from the 1972 Anti-Ballistic Missile Treaty. Last year, Putin suspended cooperation on the Treaty on Conventional Armed Forces in Europe, which limited the number of conventional armed forces that may be deployed in Europe.

"If there is no agreement on a new START treaty and Russia withdraws from the INF Treaty, all that may be left of arms control in a few years is the 1963 test ban treaty -- which would give rise to great concern," said Angela Stent, a professor at Georgetown University.

The INF Treaty, or the Intermediate-Range Nuclear Forces Treaty, was condemned by Putin last year as a relic that no longer served Russia's interests. Putin's announcement came in response to plans by the Bush administration to install 10 interceptors in Poland and a radar installation in the Czech Republic -- components of a missile-defense shield that the Kremlin views as a threat to Russia. Missile defense will be discussed Sunday in Sochi.

The Partial Test Ban Treaty of 1963 prohibits all nuclear weapon tests except those carried out underground. Another key treaty, the Comprehensive Nuclear Test Ban Treaty, which bans all nuclear explosions, has been signed but not ratified by the United States.

Many observers say Bush has been distracted by the war in Iraq. "Mr. Bush thought Russia would not be any trouble for the U.S., and he was so busy with Iraq, Iran and North Korea that he did not pay an appropriate amount of attention to Russia," a Western diplomat said.

So when Putin invited Bush for informal talks in Sochi, Bush accepted the invitation, even though some aides advised him to pass, the Kremlin said.

Bush "doesn't want to be remembered as the president who destroyed the relationship with Russia," the diplomat said.

The lack of breakthroughs in virtually every area comes despite the impressive amount of time and effort that Bush and Putin have invested in their relationship. This failure, critics said, is because they have relied on their personal relations. "Leaders tend to come and go," said Alexander Konovalov, head of the Institute of Strategic Assessments.

A senior Foreign Ministry official said, however, that the warm personal relations have saved Russian-U.S. ties. "It is close working contacts between the heads of state that have pulled forward Russian-U.S. ties and have not let them reach a freezing point," the official, Alexander Kramarenko, wrote in a commentary in Kommersant this week.

The first meeting between Bush and Putin took place less than five months after Bush assumed office, on June 16, 2001. Putin had already been president for more than a year. It was at this U.S.-Russia summit in Ljubljana, Slovenia, that Bush famously declared that he had gotten a sense of Putin's soul. Bush also said Russia and the United States should "establish a new relationship beyond that of the old Cold War mentality."

Progress, however, has been so slow that Bush apparently felt compelled to repeat this mantra Wednesday. In a speech at a NATO summit in Bucharest, Hungary, Bush said he would tell Putin in Sochi that Russia was not an enemy.

The agreement that Bush and Putin hope to sign on Sunday would provide a road map for the transitional period during the change of leadership in Russia and the United States and for the medium-term future, the Kremlin said.

While Putin in his postpresidential capacity as prime minister could make sure the agreement was fulfilled, the new U.S. administration would be under no legal obligation to honor it, analysts said. Still, any agreement could be helpful. "They can't be simply dismissed out of hand," Kuchins said.

For Bush, the informal Sochi summit will be his seventh visit to Russia, the Kremlin said. Putin has visited the United States four times. The Kremlin said Putin and Bush had met 26 times, with their last two visits planned for Friday during a Russia-NATO Council meeting in Bucharest and in Sochi.

The Associated Press reported that Bush had met with Putin more often than with any other leader except Blair, the former prime minister of Britain. The report said the U.S. and Russian presidents had met around 20 times.

A U.S. administration official confirmed that Putin is among the leaders whom Bush has met with most. She could not say how many times Bush and Blair had met.

While Bush has stopped in Moscow, St. Petersburg and Pushkin, outside St. Petersburg, the visit to Sochi will be his first. Putin invited Bush to Sochi in 2003, when he welcomed Bush's father, former U.S. President George Bush to the villa.

Bush is likely to enjoy his stay there. Just as Bush calls his getaways to his Texas ranch "working vacations," Putin likes to take his work to the beach, conducting meetings there with heads of state and Cabinet members. Located among pine trees a short walk from the beach, the Bocharov Ruchei residence was built after Stalin's death for vacationing Communist leaders. Yugoslavia dictator Josip Broz Tito was one of its most famous foreign guests.

With Putin obliged to play the good host in Sochi, he will refrain from confrontational rhetoric during Friday's meeting of the Russia-NATO Council, a Kremlin official said. "If we start calling them earthworms in Bucharest, it would not be good," the official told Izvestia, borrowing a phrase from Rudyard Kipling's "The Jungle Book."

Few want to speculate what Russian-U.S. relations might look like after Putin and Bush step down. "We are not a weather forecast bureau," Foreign Ministry spokesman Boris Malakhov said. "We'll watch American policies and construct our own."

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Bush-Putin Visits

1. June 16, 2001: U.S.-Russia summit, Ljubljana, Slovenia

2. July 20-22, 2001: G8 summit, Genoa, Italy

3. Oct. 21, 2001: APEC summit, Shanghai

4. Nov. 13-15, 2001: Putin's first visit to the U.S. White House, Bush's ranch in Crawford, Texas

5. May 24-26, 2002: Bush's first visit to Russia. Moscow, St. Petersburg

6. May 28, 2002: Russia-NATO Council, Rome

7. June 27, 2002: G8 summit, Kananaskis, Canada

8. Nov. 22, 2002: Bush's second visit to Russia. St. Petersburg

9. June 1, 2003: Bush's third visit to Russia. 300th anniversary of St. Petersburg.

10. June 1-3, 2003: G8 summit, Evian, France

11. Sept. 26-27, 2003: Putin's second visit to the U.S. Camp David, Maryland

12. Oct. 20-21, 2003: APEC summit, Bangkok, Thailand

13. June 6, 2004: 60th anniversary of D-Day, Cannes, France

14. June 9, 2004: G8 summit, Sea Island, Georgia

15. Nov. 20, 2004: APEC summit, Santiago, Chile

16. Feb. 24, 2005: Russia-U.S. summit, Bratislava, Slovakia

17. May 8-9, 2005: Bush's fourth visit to Russia. 60th anniversary of end of World War II, Moscow

18. July 7, 2005: G8 summit, Gleneagles, Scotland.

19. Sept. 16, 2005: Putin's third visit to the U.S., Washington.

20. Nov. 18, 2005: APEC summit, Busan, South Korea

21. July 14-17, 2006: Bush's fifth visit to Russia. G8 summit, St. Petersburg

22. Nov. 15, 2006: Bush's sixth, brief visit. Moscow's Vnukovo Airport

23. Nov. 19, 2006: APEC summit, Hanoi, Vietnam

24. June 6-8, 2007: G8 summit, Heiligendamm, Germany

25. July 1-2, 2007: Putin's fourth visit. Bush's family house, Kennebunkport, Maine

26. Sept. 7-9, 2007: APEC summit, Sydney, Australia

27. April 4, 2008*: Russia-NATO Council, Bucharest, Romania

28. April 5-6, 2008*: Bush's seventh visit. Putin's vacation residence, Sochi

*Scheduled

Source: Kremlin