When British Prime Minister Tony Blair asked President Bill Clinton three years ago for guidance on dealing with a successor, Clinton offered some succinct advice: "Be his friend."

"Friendship" may seem like a strange word for world leaders, who are responsible for representing the interests of their nations when they meet at events such as this week's Group of Eight summit in Sea Island, Ga. But personal bonds can help smooth out rough patches when national interests conflict -- or sometimes cause a blind spot when a cold assessment is required.

Clinton forged links with leaders who had similar outsized appetites and personalities, and he generally did not let disputes over policy interfere with those personal relationships. In President Bush's case, the relationships are very much on his terms, said former and current officials, as well as officials overseas.

Bush bonds with leaders who see the world as he does, who in his view "get" the war on terrorism, who talk simply and straightforwardly and do not break any private commitments and understandings, officials said. Leaders who are willing to accept his point of view may be able to modify it somewhat, or gain something in return, but those looking for real negotiations or give-and-take are liable to come away disappointed, officials and diplomats say.

According to one former White House official, Bush appears to have a simple test for evaluating his fellow leaders: Good people or bad people? Do they have a vision for their countries or not?

"Whenever he talked about leaders, these were the categories he used," said the official, speaking on the condition of anonymity. He said a CIA official who regularly attended the president's daily intelligence briefings first pointed out to him Bush's use of these terms, which was then confirmed by his own experience as a senior policymaker in the White House.

Beginning with the G-8 summit this week, Bush will socialize and negotiate with key leaders at a series of high-profile summits this month. The stakes are high for the president, who is seeking to win international approval for the U.S. plan to grant some political authority to an interim Iraqi government that will lead the war-torn nation until elections next year.

Bush has had mixed relations with the world leaders who will gather this week. Among them will be two, Blair and Japanese Prime Minister Junichiro Koizumi, who have given much thought to understanding Bush's personality and his approach to the issues. Both have assiduously courted him because they believe their nations' interests are enhanced by a close relationship with the American president.

Blair immediately figured out how important missile defense was to Bush at the start of his presidency -- and leveraged that to forge a common position on a range of issues. Koizumi backed Bush to the hilt on Iraq, even taking the unprecedented pledge of sending Japanese troops there. Koizumi's loyalty helped ensure Bush's acceptance of his trips to North Korea.

On the other hand, Bush has never really clicked with French President Jacques Chirac and German Chancellor Gerhard Schroeder. After a G-8 summit in Canada two years ago, a former U.S. official recalled, Bush told his aides in the White House situation room that Chirac just didn't "get" the war on terrorism. By contrast, he lavished praise in the same meeting on Italian Prime Minister Silvio Berlusconi -- who will also attend this summit -- for understanding the terrorism threat.

Meanwhile, Schroeder's decision to oppose the war in Iraq to ensure his reelection -- after Bush believed he had promised to support it -- made it difficult for the president to trust Schroeder again.

Over the weekend, the continuing testiness between Bush and Chirac was on full display during a joint news conference in Paris. Chirac insisted he was never convinced there were weapons of mass destruction in Iraq -- and told Bush that before the war -- and also scolded Bush for comparing the Iraq war to World War II.

But the common struggles and stresses of leadership these leaders face sometimes helps bridge the gap. When the space shuttle Columbia blew up two months before the Iraq war started -- and the United States and France were at diplomatic loggerheads -- Chirac immediately called Bush and spoke emotionally about the tragedies that heads of state sometimes had to face. Before hanging up, Chirac told Bush he was praying with him over the accident, a French official said.

Bush puts a lot of stock in his gut-level assessments of his fellow leaders. The fact that Russian President Vladimir Putin treasures a cross given by his mother -- and had it blessed in Israel -- convinced Bush he could deal with the former KGB operative. As a result, Bush declared after their first meeting that Putin was "very straightforward and trustworthy" and he was able to "get a sense of his soul."

Since then, Bush has continued to have close relations with Putin, who also will attend the summit, even as questions have arisen about whether Putin was smothering Russia's fragile democracy. National security adviser Condoleezza Rice said yesterday that the relationship is "so broad and deep, the presidents could talk about anything on the map" when they meet at the summit.

A close look at Bush's relations with four leaders from different regions of the world -- Britain's Blair, Mexico's Vicente Fox, Japan's Koizumi and Israel's Ariel Sharon -- offers insights to how Bush will operate during this critical diplomatic period.

The White House declined to make an official available to speak about the president's views on foreign leaders, or to respond to a list of nearly 20 questions about specific examples in this article.

Blair: Same Wavelength

Blair was extremely close to Clinton, a fellow political centrist, and much of his staff -- and his wife, Cherie Blair -- were furious that Bush won the disputed 2000 election over Clinton's vice president, Al Gore. But that did not stop Blair from carefully studying Bush and figuring out what he wanted, British officials said.

So, on his first visit to Washington to meet with Bush, Blair arrived with a proposal: He would support Bush's plan for a missile defense system -- which most European countries vehemently opposed -- if Bush would agree to negotiate a deal ending the Anti-Ballistic Missile Treaty with Russia instead of pulling out unilaterally. Bush eventually adopted Blair's idea. The Camp David meeting, best known for Bush's comment that the two men had much in common because they both used Colgate toothpaste, set the stage for their working relationship.

Blair sees himself as a bridge to Europe for Bush, and he works to dull the sharp edges of the administration's unilateral tendencies. In the run-up to the war with Iraq, Blair helped Bush make midcourse corrections in a bid to win greater international support -- though, in the end, the effort largely failed.

Bush and Blair now closely coordinate their policies. Blair writes long letters to Bush -- it is unclear whether Bush writes long letters back -- and the two leaders frequently communicate via a secure video link between the White House and the basement of 10 Downing Street, the prime minister's residence.

The two couples have also mixed it up. Philip Stephens, associate editor of the Financial Times and author of a sympathetic biography of Blair, said that Cherie Blair, a noted lawyer, once confronted Bush as the two couples dined together about his frequent use of the death penalty as Texas governor. At the same meal, Stephens said, Laura Bush confided that she disagreed with the president's opposition to abortion.

As Blair's poll ratings have sunk because of the turmoil in Iraq, a number of his advisers have counseled the prime minister to distance himself from Bush. But Stephens said Blair is irritated by this advice, arguing that a relationship with a U.S. president is "not a balance-sheet exercise." Pressed on how Bush has accommodated Blair's concerns, Blair will frequently cite the Middle East peace process, such as persuading Bush to accept the now-stalled peace plan known as the "road map."

"Blair would say he's been influential" on the peace process, Stephens said. "What I would say is: If that is influence, what is it worth?"

Fox: No Big Advantage

The budding romance between Fox and Bush died with the Sept. 11, 2001, attacks.

Days before the attacks, the Mexican president and two of his advisers, Adolfo Aguilar Zinser and Jorge Castaneda, flew on Air Force One with the president. Aguilar Zinser recalled a very relaxed Bush telling them: "I feel much more comfortable around you guys" than other world leaders. Bush offered them beers, serving a nonalcoholic one to himself. Loose, candid and comfortable, Bush talked excitedly about what an affinity he had with Mexico's new leadership.

At the White House ceremony on Sept. 5, Fox even boldly declared the two men would reach agreement by the end of the year on a broad new program for work visas for migrants.

But three years later, it is clear that Fox's friendship with Bush has not brought Mexico any real advantage. A Mexican official, who asked not to be identified, said that he believes Bush and Fox are friends, but that what has changed is Bush's focus. At the outset of Bush's presidency he said Washington had no more important relationship than the one it had with Mexico. But after Sept. 11, his focus turned to the war on terrorism.

In 2001, Fox had just been elected and captivated worldwide interest as the democratic leader who defeated the authoritarian party that led Mexico since 1929. Now, the official said, Fox is perceived as someone who cannot deliver what Bush wants -- such as a critical vote on the U.N. Security Council supporting war against Iraq -- and Bush no longer sees him as a "go-to guy." The official said: "In 2000, Bush needed Fox. Now he doesn't."

Despite the change in the dynamic of their official relationship, Fox and Bush remain friendly, in part because they both "ooze that their religion deeply affects them," one official said. Fox is a Roman Catholic who attends Mass each week. During meetings, Bush and Fox each have talked about their mothers and family, according to those in the room with them. "I think there is deep empathy between the two," another government official said.

Still, Aguilar Zinser said, the Bush-Fox relationship fits the tradition for Mexico that being well-received in Washington does not translate into "a cutting-edge advantage."

Koizumi: Good Chemistry

Koizumi, who has broken the mold of the cautious Japanese politician, has hit it off with Bush since their first meeting in June 2001. Koizumi usually dispenses with the talking points prepared by the Foreign Ministry bureaucrats and instead pushes the issues that interest him.

"They speak very freely," said a senior Japanese official who has attended meetings between Bush and Koizumi. "What Koizumi says is very 'human.' He speaks with different tones of voice, and he laughs a lot during the meeting. He is very honest with himself and conveys that very straightforwardly. And that mannerism suits Mr. Bush, too."

In policy terms, this has made a difference, particularly on the Japanese side. Where cautious bureaucrats might have once seen red lights from their leadership, they now only see green lights, U.S. and Japanese officials said. In fact, lower-level Japanese officials now have more incentive to resolve issues with American counterparts to avoid having them handled by their unpredictable leader. As one official put it, "the bureaucrats know that if a matter goes to the two leaders they know what would happen" -- Koizumi will agree to Bush's request.

Koizumi also has a raw sense of humor. During a meeting in Crawford, Tex., in 2003, the two men sat by the pool for several hours, with only interpreters. At one point, Koizumi mentioned he had listened to an Elvis Presley song the previous day. "Usually people stop there. But Koizumi actually started to sing the song," the official said. "That lack of formality is what Bush likes about Koizumi. Koizumi is Japan's Texan."

In the past three years, Koizumi has been a strong supporter of Bush's major policies -- the fight against terrorism, the wars in Afghanistan and in Iraq, the strategy to restrain North Korea's nuclear arms programs, and the missile defense initiative. Under Japan's pacifist constitution, sending Japan's Self-Defense Forces overseas is highly controversial. But Koizumi provided swift logistic support for U.S. forces during the Afghanistan conflict; he also sent troops to southern Iraq to provide humanitarian and reconstruction assistance.

In return, Koizumi has won Bush's blessing to pursue talks with North Korea over the fate of Japanese hostages. The White House initially was blindsided by Koizumi's plans to visit Pyongyang in 2001. Before Koizumi departed, Bush privately warned him that the United States possessed new intelligence showing North Korea has a secret uranium program. That intelligence led to the current crisis over North Korea. More recently, Bush quickly approved Koizumi's plan to return to Pyongyang last month.

"There is a tolerance Bush has for elements of Koizumi's rapprochement with North Korea he wouldn't tolerate with anyone else," said Charles L. "Jack" Pritchard, until last year senior envoy for negotiations with North Korea.

Sharon: Not a Schmoozer

Bush had met Sharon before he became president, when as governor he took a tour of Israel that included Sharon's standard helicopter ride to show the insecurity of Israel's borders. But even that initial encounter did not help break the ice when they had their first meeting at the White House early in 2001.

David Ivry, then the U.S. ambassador to Israel, recalled that Bush tried to bring up personal issues during the lunch. "President Bush very much wanted to go beyond political issues," Ivry said. But whenever Bush tried to bring up a subject not related to politics, "Sharon heard it and went back to political issues immediately."

But one key issue was settled at that first meeting: an understanding that Sharon would not do anything to harm Palestinian leader Yasser Arafat. A few weeks ago, when Sharon hinted he was no longer bound by that understanding, Bush reacted in fury and Sharon quickly retreated.

But generally Sharon works hard to stay in Bush's favor. Sharon, in fact, "sees as his signal achievement that he has avoided crossed wires with Bush," said David Makovsky, an analyst at the Washington Institute for Near East Policy who is in close contact with Israeli and American officials. "The question of his credibility is important for Sharon."

Under Bush's simple calculus, however, Sharon for much of his term was a good person with little or no vision. That assessment changed, U.S. and Israeli officials say, when Sharon earlier this year presented Bush with his plan to vacate Gaza and part of the West Bank.

Bush's willingness to embrace Sharon's "vision" -- in particular, the demand for letters outlining U.S. concessions to Israel's negotiating position with the Palestinians -- has caused a fierce backlash in the Arab world and to some extent has eroded Bush's other goals in the Middle East.

The Israeli-Palestinian conflict, in fact, is so politically sensitive, both domestically and internationally, that the two men carefully plot their formal meetings. Administration officials, however, recall one unscripted exchange between the two men. Bush had called Sharon a "man of peace" in 2002, infuriating Arabs. During a meeting months later, when the Israeli leader -- who tends to speak in platitudes in the formal sessions -- began to say he was a "man of peace and security," Bush pounced.

"I know you are a man of security," Bush said, according to a witness to the conversation. "I want you to work harder on the peace part."

Then, using colloquial language that seemed to baffle Sharon, Bush added: "I said you were a man of peace. I want you to know I took immense crap for that."

British Prime Minister Tony Blair, with President Bush at the White House, is one foreign leader who believes that his nation's interests are enhanced by a close relationship with the American president.