(FORTUNE Magazine) – After 13 years of legal back-and-forth, the trial that promises to be one of the most sensational in business history has begun in a Topeka federal courtroom. Koch v. Koch not only pits brother against brother (even twin against twin), but also calls into question the corporate philosophy of one of the world's most successful CEOs.

When Charles Koch took over Wichita-based Koch Industries in 1967--the year his father, the founder, died--the family-owned oil and ranching company's sales totaled $177 million. It is now the second-largest private U.S. company, and revenues from its oil, finance, chemicals, and agriculture businesses bring in $35 billion a year--more than Microsoft or PepsiCo.

While Charles, 62 and still CEO, receives the credit for that 19,674% growth, he has otherwise managed to keep a low profile. By most accounts--especially in the local press--Charles is a bookish, conservative businessman long on humility and hard work. "He's probably one of the nicest people I've ever met, just a very decent, honest guy," says Jerry Ellig, a George Mason University economist who worked with Charles.

But that flattering image is now being challenged. In a case locked up in pretrial appeals since it was filed in 1985, Charles' brothers (worth $1 billion-plus between them) are suing Charles and Bill and Frederick(an executive VP and Bill's fraternal twin) over the value of the company's stock. Bill and Fred claim that they, along with minority shareholders, were cheated out of more than $1 billion when they sold their 48% stake in the company for $1.1 billion in 1983. They accuse their billionaire brothers--who now own 80% of Koch Industries--and other Koch executives of concealing information that would have raised the stock price.

In his opening statement on April 8, Fred Bartlit, the attorney representing Bill, called CEO Charles a man whose "driving need for total control and total power" led him to cheat his own brothers. "Charles Koch is a man of two faces," Bartlit told the jury. "He will testify with the charm of a master salesman," but in private he "demands total control, total obedience." Charles' lawyer called Bartlit's depiction "creative writing." (A gag order is in effect for both sides.)

What makes Bartlit's characterization so provocative is that it contradicts not only Charles' image and libertarian views (he and David co-founded the libertarian Cato Institute) but also the free-market values and "market-based management" system he has used to run the company for the past 31 years. Market-based management is intended to decentralize corporate structure and to distribute decision-making power--in short, it's the kind of management most power-hungry CEOs despise.

No matter who wins, no one expects this to be the last battle in the Koch brothers' legal war. Many people, including the presiding judge, think the case is more about sibling rivalry than money, and an appeal is almost certain. But if Bill's side shows convincing evidence that Charles is truly a corporate autocrat, Koch's image--the man and the company--will never be the same. And those power-hungry CEOs will rest easy knowing that they've been doing it right all along.

--Erin Davies