A hedge fund allegedly gained unfair trading privileges at several big-name mutual fund companies--including Bank One's investment arm--in an illegal arrangement that law enforcement officials say is widespread and could be costing investors billions of dollars.

Canary Capital Partners LLC, a multimillion dollar hedge fund, and its managers agreed to pay $30 million restitution for illegal profits generated from unlawful trading and a $10 million penalty, New York Attorney General Eliot Spitzer said Wednesday.

In exchange for big-money investments, Spitzer said, several mutual funds bent the rules applied to most investors and allowed Canary to make after-hours trades and short-term ''in and out'' deals. Canary arranged to make such trades with several leading mutual fund families--including Bank One's Banc One Investment Advisors, Bank of America's Nations Funds, Janus and Strong.

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Mutual fund companies state in their prospectuses that they discourage or prohibit ''late trading'' and short-term ''market timing'' by large investors. But Spitzer's investigators found evidence that mutual fund managers permitted certain companies to conduct such trades in exchange for payments and other inducements.