NEW YORK (CNN/Money) - The New York Stock Exchange is investigating whether at least two of the largest floor-trading firms may have engaged in trading shares ahead of clients, or "front-running," in a possible abuse of a central part of the market's trading system.

The NYSE confirmed Thursday that it is looking into the trading practices at several of the specialist firms.

"While Exchange policy precludes us from commenting on regulatory matters, the NYSE does confirm that, as part of its ongoing commitment to surveilling the marketplace, it is conducting a review of trading practices at several specialist firms," the Exchange wrote in a prepared statement. "Consistent with our policy, if wrongdoing is found, the Exchange will release that information publicly once the investigation and the prosecutorial process is completed."

The New York Stock Exchange is investigating possible trading floor abuses. CNNfn's Susan Lisovicz explains what NYSE specialists do and why some are suspected of front-running. Play video (QuickTime, Real or Windows Media)

Specifically, the NYSE is examining whether the specialist firms, whose floor traders carry out clients' orders, had offered inferior prices to investors who send orders to buy or sell shares through the exchange's main trading system, according to the Wall Street Journal.

If any wrongdoing is found it could be add another blow to investor confidence, already shaken by the accounting scandals at Enron, WorldCom, Global Crossing and other firms.

The NYSE's inquiry is focused on at least two of Wall Street's biggest names -- FleetBoston Financial Corp.'s Fleet Specialist unit, and LaBranche & Co., the newspaper reported. The NYSE has seven specialist firms.

Subsequent to the NYSE probe, Fleet Specialist's management suspended specialist David Finnerty earlier this week, a source familiar with the situation told CNNfn. At the firm's daily morning meeting Thursday, Fleet management said that Finnerty's situation "is an internal Fleet matter."

Finnerty handles Fleet's trading for General Electric Co. (GE: Research, Estimates) stock on the NYSE floor, according to the Journal. The paper reported that Finnerty was suspended by Fleet Specialist's CEO Christopher Quick, who also is a director of the New York Stock Exchange, according to its Web site.

As part of its own investigation, Fleet is examining whether 37-year-old Finnerty had traded ahead of customer orders in GE, which boasts the world's biggest stock-market capitalization of around $276 billion.

According to the Journal, it is not clear how much money would have been involved in any alleged front-running, or how many of the specialists' clients might have been affected.