Aker ASA, founded in 1841, is Norway's largest private employer, with around 35,000 employees and annual revenue of roughly $10.90 billion. But until 2004, the company had no female directors.

Today, the industrial holding company has three, and women occupy 13 more seats on the boards of six companies in which Aker holds significant stakes.

What happened? A 2003 law requires every publicly traded company in Norway to have a certain number of women on its board by Jan. 1 or risk being shut down. Exactly how many depends on the board's size, but nationally, the law -- the first of its kind in the world -- aims for women to hold 40% of such directorships.

The law is already reshaping Norwegian boardrooms. As of early December, women now occupy nearly 35% of the seats at the roughly 500 companies covered by the law, up from nearly 7% in 2002. By contrast, in the U.S., women hold 14.8% of the board seats at the 500 largest companies, and 59 of those concerns have no female directors, according to a report being released today by Catalyst, a New York research group.

As the law's deadline nears, the scramble for female directors is intensifying. The U.S. search firm Korn/Ferry International says nearly every Norwegian assignment it has had in the past two years has involved finding a female board member. Norwegian citizenship isn't a requirement, but it helps if directors speak Norwegian because it's generally used at meetings and in board documents.

Prominent Norwegians are in particular demand. Thorhild Widvey, a former minister of oil and energy, has taken 11 corporate board seats, five of them at publicly traded companies, since leaving government in 2005. She spurned about 40 other offers, and is busy enough and earning enough -- nearly $91,000 last year -- that she no longer has a full-time job.

A public database where any woman could nominate herself has attracted preschool teachers, engineers and others with unconventional credentials. To train women to be directors, a major employer group called the Confederation of Norwegian Enterprise created a Female Future project. So far, 590 women have participated, though only about 34% have landed board spots.

Not everyone is happy with the law. Trygve Hegnar, CEO and editor-in-chief of Hegnar Media, publisher of Norway's biggest financial newspaper and newsmagazine, says boards have "kicked off some very good" members to make room for inexperienced newcomers whose "main qualification is that they are women."

The 64-year-old, white-haired media mogul has unsuccessfully sought a board seat at Gyldendal ASA, owner of a major book publisher, since acquiring a 29% stake in 2003. Women snared both board vacancies during the period.

"I am not going to change my sex to qualify," fumes Mr. Hegnar, his arms crossed as he perches on a throne-like yellow chair surrounded by antique ship figureheads. During a recent lunch with Erik Must, Gyldendal's chairman and largest shareholder, Mr. Hegnar says he repeated his demand, but Mr. Must told him, " 'We can only have one more [director], and it has to be a woman.' " Mr. Must didn't return calls seeking comment.

Gyldendal shareholders elected a third woman director last week, bringing the company into compliance with the law, a spokesman says. About 32% of the votes cast favored Mr. Hegnar's candidacy, the spokesman adds, but only 900 of those 682,267 votes came from investors other than Mr. Hegnar.

Rather than comply with the gender law, more than 30 affected companies are going private, says Grace Skaugen, an investment banker turned professional director and recruiter.

Meanwhile, government officials won't say how they will handle companies that miss the deadline. Marit Hoel, managing director of the private Center for Corporate Diversity here, estimates that between 80 and 100 companies will fall short of their target by early January. That would force the government to choose between closing them and ignoring the law. It's "a nerve-wracking situation for the government," Ms. Hoel says.

Dag Terje Andersen, Norway's minister of trade and industry, whose department monitors compliance, says companies with too few women in their boardroom on Jan. 1 "will have a lot of opportunities to use common sense" and add women. "I am quite optimistic we won't come to" shutting companies, he says.

At Aker, the board historically was "a club of old men. If you put me on your board, I'd put you on mine," says Gerhard Heiberg, a former Aker president.

Aker opposed the 2003 law because "we think shareholders should make these decisions, not the government," says Bengt A. Rem, chief financial officer. After the law passed, however, Mr. Rem says, "We made the best of it."

Aker's task was particularly complicated because in addition to its own all-male board, it eventually had to find women for six publicly traded businesses in its portfolio. Aker created a shareholder-selected nomination committee, separate from its board, that included Mr. Heiberg. He began seeking a woman for the board of a portfolio company even before the law passed.

Mr. Heiberg says he largely looked abroad because he feared prime Norwegian prospects would quickly be overcommitted. Acquaintances helped him compile a list of high-level corporate women in Denmark, Sweden and Finland. His first recruit was Lone Fønss Schrøder, a veteran Danish shipping executive. She first joined the board of the Aker portfolio concern, later joined Aker's board, and is now deputy chairman. "She has brought a lot of international experience" to boardroom discussions, Mr. Heiberg says.

Ms. Schrøder, currently president and CEO of Wallenius Lines in Sweden, thinks her broader view helped Aker cope with a difficult restructuring and expand in the Far East. "The company had been a very, very Norwegian company," she recalls. "Now, it is more of an international company."

Several Norwegian women on Aker boards recommended others from their budding "old girls' network." Ms. Widvey suggested Kristin Krohn Devold, a fellow former Conservative member of Parliament. Mrs. Devold joined the board of a company partly owned by Aker in 2006 and Aker this year.

When two more companies in which Aker has stakes start trading their shares next Monday, women will account for about 42% of investor-elected directors at nine Aker concerns. Directors elected by employees are exempt from the law when one gender dominates the work force.

Unwilling to enlarge its boards, Aker sometimes bumps men to make room for women. Geir Arne Drangeid, an Aker executive vice president, was a director of an Aker-affiliated firm for a year but wasn't renominated this year. "Me leaving was a convenient way to obtain the necessary gender equality on the board," he says.

Mr. Heiberg believes the addition of so many female directors has improved Aker's corporate governance. Ms. Widvey, for example, has "good contacts in politics, business and industry," he says.

Men now do more homework before board meetings because they want to impress their female colleagues, he adds. "This is human nature."