Since being named BP’s CEO, effective Oct. 1, Bob Dudley has already displayed the deftness that made him the obvious replacement for Tony Hayward. Consider one example: Not long after halting the gulf oil leak, the embattled oil giant was poised to declare its return to profitability — $1.8 billion for the third quarter of 2010. To keep the news from becoming a political issue, Dudley shrewdly postponed the announcement for a week, until Nov. 2 — the date of the U.S. midterm elections.

The first American to run BP, Dudley, 55, faces enormous challenges: rounding up $40 billion to pay for the gulf disaster, restoring BP’s tattered reputation, running the world’s fourth-largest business, and, of course, avoiding another catastrophe. As Dudley acknowledged in a November interview with Fortune, the stakes couldn’t be higher: “We can’t afford another event or incident like this as a company.”

He’s been on the hot seat before. Raised in Mississippi and trained as a chemical engineer, Dudley landed at BP when it merged in 1999 with Amoco, where he’d helped plot strategy. At BP, he then worked a career-boosting turn as one of former CEO John Browne’s “Turtles,” a hand-picked deputy who learned at the boss’ side. But it was in Russia that Dudley proved his mettle, during five years as the first CEO of TNK-BP, the company’s joint venture there, formed in 2003. Under Dudley, TNK-BP became a lucrative business, providing about a third of BP’s oil production. In 2007, when Browne resigned, Dudley’s performance put him on the list of finalists for the job that then went to Hayward.

Dudley remained at TNK-BP but soon became a target of harassment by BP’s Russian partners, who wanted more control over the fifty-fifty venture. Russian authorities raided the TNK-BP offices and refused to renew Dudley’s visa, eventually forcing him to flee the country and go into hiding. Dudley spent the next five months running TNK-BP from three different secret locations, before Hayward resolved the standoff with a settlement that maintained the company’s financial interest but gave the Russians more operating control and required Dudley’s resignation.

While taking four months off after this “pretty traumatic” experience, Dudley received several CEO offers. Instead, he stayed with BP (BP), joining BP’s board in 2009 and serving as Hayward’s “secretary of state,” a roving international emissary for thorny problems. He was in India when he got Hayward’s call summoning him to the Gulf of Mexico. Dudley returned home to London, packed some fresh clothes, and flew to Houston, where he remained for months.

Soon after the explosion of the Deepwater Horizon, some of Hayward’s advisers urged him to let Dudley — who retains a touch of a Southern accent — serve as BP’s American face, a move that, in retrospect, might have saved Hayward’s job. But Hayward insisted on handling the crisis personally — until BP’s board made the decision for him, first making Dudley point man on the gulf response, then naming him as CEO.

During the interview with Fortune, Dudley pointedly refused to criticize his predecessor. He says BP’s spill response “was exactly what the company needed and what the Gulf Coast needed.” As for Hayward’s gaffes? “There were probably three or four sentences that were taken wrong and that created that lightning rod.” Dudley says he understands the fear that pervaded the Gulf Coast. With no certain end to the leak in sight, he notes, “this was in some ways an infinite event.”

At BP headquarters in London a month after Dudley took over, there were few visible signs of change. A wall still displayed the sign Hayward had installed as “a bit of symbolism”: Mirroring postings usually found in industrial worksites, it provided a daily update on the number of “safe days worked at BP headquarters.” (As of Nov. 3, the tally read 1, 167.) Upstairs, a framed copy of BP’s safety motto — “No accidents, no harm to people, and no damage to the environment” — still bore the name of Tony Hayward, CEO.

But Dudley wasted no time making bigger changes. He named Mark Bly, who led the company’s internal probe of the Horizon explosion, chief of a new safety division with broad powers. The company’s two top exploration and production executives are now gone. Dudley also sought to deliver an unambiguous message throughout the company: For the fourth quarter of 2010, all bonuses would be based solely on their success in meeting safety goals. Dudley says he intended the step “to remove anybody’s being put in the place of driving for performance vs. safety … I’m not saying that’s what’s out there, but it’s just [to] remove anybody trying to make that tradeoff … I’m a big believer that you get the behaviors that you incentivize.”

Like Hayward, Dudley says the Horizon accident illustrates problems facing “the industry all over the world,” and resulted, as he puts it, from “a unique combination of failures, of equipment, judgment, people  … There’s multiples causes.” He adds: “I do not believe BP is an unsafe company.” Yet Dudley rejects the notion that the industry needs tougher regulation, even while remaining diplomatic about that prospect. “All the companies want to do this in a very responsible way,” he says. “It’s good business to do that. I think that companies will
respond themselves, and they do that in concert with the regulatory environment as well … I think the oil industry has been good over its history of developing high standards itself  … But obviously, we just need to learn the lessons from this accident.”

Does that require stronger regulation? “ ‘Strong’ isn’t the right word,” replies Dudley. “But it definitely needs to change  … I don’t think the companies should be afraid of that. I mean, as long as the regulatory process is reasonably efficient, that allows business to be done in a safe way, that’s a win-win for society and people.”
Dudley has also made considerable progress in selling assets to fund BP’s costs for the accident, striking deals for nearly $22 billion out of a planned $30 billion in divestments. At the same time, he has announced a handful of new exploration projects — most recently, in Russia.

In mid-January, Dudley announced a “historic” new alliance with the state-owned Russian oil giant Rosneft. Together the two companies will drill for oil and gas offshore, in the previously unexplored Russian Arctic. The two companies cemented their alliance with an extraordinary international stock swap. After a private meeting with Dudley, Russian Prime Minister Vladimir Putin even gave the deal his personal blessing.

Doing business in Russia is always dicey, as Dudley’s previous experience makes clear. The Financial Times wryly remarked that “BP and Russia have embraced each other like two drunks leaning together for support.” But for BP, the potential upside — replacing much of the reserves it has been forced to sell off — was irresistible. It was widely regarded as a coup for the new CEO.

The deal resulted from a series of post-spill trips to Russia — and Dudley’s ability to minimize even bitter conflict. In November, Dudley told Fortune that after being named CEO, his old Russian associates had assured him his rough treatment at TNK-BP was “never personal” — simply “business.” Dudley says the Russians praised him for never publicly detailing their differences. (He wouldn’t even allow Fortune to name the countries where he went into hiding.)

“ ‘The fact you never talked about it and never complained means that we can work together,’ ” Dudley says the Russians told him. “I think that’s a good, good lesson in life,” BP’s CEO adds. “Never burn a bridge like that.” For BP, that’s an important start.

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