Six Flags, which said in August it was for sale, has received takeover interest from about three dozen prospective buyers, many of them private equity firms. The company, whose financial records have been disclosed to possible buyers, has a market capitalization of about $674 million and debts of more than $2 billion.

Stacy Frole, director of investor relations for Cedar Fair, said her Sandusky company has financial wherewithal to buy Six Flags or some of its parks. But the deal would have to make financial and strategic sense, she added.

"If the price is right, we'd go for it," she explained. "This has been going on for a month or two, but Six Flags has only made its financial information available now. Until we look at it, we can't say what we will do."

Such a move would be a departure for the Lake Erie amusement business, which has struggled this year with attendance at some of its parks. Historically, the company has acquired only one park at a time.

Six Flags, of Oklahoma City, has 28 theme parks or water parks in the United States, plus one theme park each in Canada and Mexico. However, only its Magic Mountain theme park in Los Angeles competes in the same market with a Cedar Fair park, Knott's Berry Farm.

A dissident Six Flags shareholder, Daniel Snyder, said two months ago he wanted to replace the company's chairman and chief executive and planned to raise his stake to 35 percent from about 12 percent. Mr. Snyder owns the Washington Redskins football team.

Company officials criticized the bid to investors. Mr. Snyder and his Red Zone LLC investment firm have not entered the auction to buy the entire company, sources said.

The auction for Six Flags comes on the heels of other recent amusement-park sales. Private equity firm Blackstone Group this year bought Legoland, which operates four amusement parks, for $459 million and European park operator Merlin Entertainment for $180 million.

Also, Dubai International Capital, the investment firm backed by the government of Dubai, bought Tussauds Group, known for its Madame Tussauds wax museums, for $1.5 billion.

Wall Street analysts expect Six Flags to fetch a high premium, given its strong brand name. For the full year, Six Flags expects to generate cash flow of $300 million and an 8.5 percent increase in revenues.

Analysts expect Blackstone and Dubai to take a look at Six Flags, but they could be turned off by the company's $2 billion in debt.

Analysts said Cedar Fair might be interested in some Six Flags properties, but it is unlikely to buy the entire company. Cedar Fair last year paid $145 million for Six Flags of Ohio, near Cleveland.