"When we were listed ... in 1996, we signed an agreement making top executives responsible for inaccurate information," said Vimpelcom vice president Valery Goldin.
"We have no objections because we always comply with all requirements," he said.
Requiring principal executives and financial officers to physically vouch for the accuracy of their quarterly and annual financial reports is part of the Sarbanes-Oxley Act. The act, passed in July, was in response to the unprecedented series of U.S. corporate fraud discoveries in the wake of the collapse of former energy giant Enron.
If executives are found to have willfully certified inaccurate reports they could face fines of up to $5 million and/or 20 years in prison. All foreign companies that submit annual reports to the SEC should also have the reports certified by top executives, said SEC spokesman John Heine. If they don't, the SEC has the right to file a civil suit.
More than 1,300 foreign companies are traded on U.S. exchanges.
Like Vimpelcom, the other three Russian companies with depositary shares traded in the United States -- Wimm-Bill-Dann, MTS and Tatneft -- were not fazed by the new rules.
Andrei Braginsky, head of investor relations at MTS, said president Mikhail Smirnov and financial director Van Bommel had already signed annual financial reports, and felt sure of their accuracy.
Tatneft, too, said it stands by its reports. "We always submit only absolutely reliable information, so we have nothing to fear. We're not Enron," said deputy general director Viktor Gorodny.
It was unclear whether the United States plans to apply the rules in full to the foreign executives: that is, fining or jailing them.
Sergei Belyak, a corporate lawyer, said it was "simply impossible" to make foreign executives responsible under U.S. law. "There is no such precedent."
Nonetheless, the possible application of U.S. law to foreigners has raised hackles in the European Union.
Frits Bolkestein, EU commissioner for internal market issues, sent a letter in July to the U.S. Senate in which he expressed concern about several provisions in the law.
German Justice Minister Herta D?ubler-Gmelin said: "Partners should either develop legislation together or acknowledge that there are different routes to the same goal."
German industrial association BDI demanded the SEC exempt German companies from the requirements of the Sarbanes-Oxley Act, but was refused.
Porsche chief executive officer Wendelin Wiedeking last week announced the company may cancel its planned listing in New York because of the act.
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