BERLIN » With a deal on Greek debt finally done, Europe will shift its attention to two of its most powerful women, friends who have dueling views about what needs to be done to prevent future Greek-like meltdowns from spreading to other economies.

The International Monetary Fund’s managing director, Christine Lagarde, who is French, finds herself on a collision course with Chancellor Angela Merkel of Germany, posing a test for the unusually close relationship between the two leaders. They have opposing stances on how much money is needed to protect vulnerable economies and how it should be raised.

Lagarde says Europe needs at least $1 trillion in emergency funds and is pressing for a much more robust European contribution before the IMF commits to raising more money from its members. She has worked hard to drag along Merkel, who is hamstrung by a domestic constituency sharply opposed to committing more money to rescue neighbors.

In spite of the sometimes tough negotiations, colleagues and confidants describe a warmth and chemistry between the two leaders that transcends policy differences. They are on a first-name basis. They frequently exchange text messages. Shortly after Christmas, Lagarde brought Merkel a trinket from Hermes and received a recording of the Berlin Philharmonic playing Beethoven from Merkel, a classical music lover.

"There are many circles and many forums where it’s only the two of us who are women," Lagarde said in an interview. "So there’s a sense of recognition, complicity, solidarity."

Yet for all that personal solidarity, the two leaders have come to represent competing philosophies for solving the debt crisis that has punished European economies and threatened the financial stability of the rest of the world.

Their opposing worldviews may well come from formative experiences. As a high school student, Merkel traveled from East Germany to Moscow to take part in a Russian language competition; Lagarde attended a prominent girl’s school in suburban Washington, complete with an internship on Capitol Hill.

Lagarde, nicknamed l’Americaine in her native France, has been vocal in support of pro-growth policies on the part of the richer European countries to help their more indebted neighbors. She has pressed Europe to make its firewalls — the pools of money available to keep borrowing rates at sustainable levels — so enormous that they scare off would-be speculators.

Since becoming the head of the IMF, and in stark contrast to her public statements in her prior job as French finance minister, she has repeatedly castigated Europe for doing too little, too late, and lacking focus on sparking higher growth rates.

Merkel, who declined to be interviewed for this article, has argued that free-spending governments got many European countries into trouble in the first place and that the path to stability runs through austerity. Large firewalls, in this view, only give countries like Greece a false sense of security and an excuse to ease up on the painful measures demanded of them. Merkel has demanded assurances that all European countries bring their finances under strict control before the governments of the European Union agree to free up resources to help.

Their differences were brought into sharp relief in January when Lagarde gave a speech at the German Council on Foreign Relations in Berlin in which she demanded that Germany step up its efforts to save the world from "a 1930s moment." Switching from her fluent English to halting, phonetic German, she concluded with a line by the German poet Goethe.

"It is not enough to know, we must apply," Lagarde told the audience. "It is not enough to will, we must do."

The speech made headlines around the world, evidence of a backroom dispute breaking out into the open. Yet Lagarde had arrived in Berlin on the eve of her address with a copy of the speech for Merkel to read before Lagarde delivered it in front of the political and foreign-policy establishment. The two women debated the crisis in private over a long dinner of veal tenderloin in the modern Chancellery’s eighth-floor dining room.

Lagarde also brought Merkel an orange-blossom-scented candle from the chic French perfumer Fragonard. The candle represented "hope," Lagarde said.

"Because we had tough discussions," she said, there "was an element of symbolism about it."

Lagarde, 56, and Merkel, 57, appear to be opposites, the glamorous, Chanel-clad French extrovert and the grounded German introvert, recently spotted doing her own grocery shopping in the same suit jacket she had worn to sign the new European fiscal pact in Brussels earlier that day.

"I’ve been in government and know what securing parliamentary support means," Lagarde said. "And equally she appreciates that I speak from a position where I have to think about not only Germany but also the whole of Europe and the stability of the international scene."

German officials are less skeptical of Lagarde, as a former French finance minister, than they are about U.S. officials, who they believe are focused on President Barack Obama’s re-election. Lagarde’s close relationship with Merkel makes it easier to bridge the gap between the United States and Germany, making her a more effective mediator.

Lagarde is "one of those policymakers that Merkel would listen to," said a French official who worked with her. "There is a relationship of trust, even if there may be issues on which their views differ."

Indeed, people close to the negotiations say German leaders have given tacit promises that Europeans will raise more money for their firewall, given enough time to build consensus in Europe. Officials also say the IMF should have little trouble raising $500 billion in lending capacity once that happens.

Analysts have noted that the austerity Merkel has pressed on other European countries has long been the IMF prescription, while tough talk from Lagarde could help Merkel sell unpopular measures at home.

"I have a suspicion that the two ladies are not as far apart as it appears, or is made to appear, in public," said Stephan Richter, president of The Globalist Research Center in Washington.

In the years it has taken to reach consensus on how to handle the crisis, critics say, the toll to business confidence, financial markets and economic growth has been unnecessarily high. Hope for a long-term solution to Europe’s debt crisis could well rest on the ability of these friends to bridge differences before Europe’s chronic problems flare up again.

Although Europeans of the same generation, Merkel and Lagarde once had lives as divided as the continent they grew up on. Separated throughout their youths by the Iron Curtain, the odds they would meet as politicians at the highest levels was improbable.

Lagarde was a member of France’s national team for synchronized swimming. Merkel needed to spend an entire swimming class mustering the courage to jump off the diving board. The prospects under Communism for a pastor’s daughter like Merkel in politics were dim at best, and she became a physicist. Lagarde became a lawyer and rose to the top of a U.S. corporate firm.

Once they entered politics, their climbs were similarly swift. Merkel was head of Germany’s largest party, the Christian Democrats, just 10 years after joining in 1990. She beat out career politicians to win the chancellorship five years later in 2005. Lagarde won the top IMF post a mere six years after joining the French government as trade minister in 2005.

The personal relationship between them was nurtured when Lagarde became the first and only member of a foreign government to sit in on a German Cabinet meeting in March 2010, taking her place across the Chancellery conference table from Merkel.

"It was a very moving moment, because she made a point of inviting me and nobody else," Lagarde said.

For Lagarde, sorting through the differences requires patience, as well as understanding for Merkel’s deeply analytical, scientific approach.

"You have to continuously explain, rationalize, dissect the whys, the pros and the cons and plead your case," Lagarde said. "It’s the lawyer and the physicist. I will continue to grit my teeth and smile and keep up the work."

© 2012 The New York Times Company