Kayak.com stopped displaying American Airlines' fares in search results after the two companies clashed over how Kayak and its subsidiary, SideStep.com, refer consumers to sites for booking American flights.

American wanted Kayak to direct consumers only to its own site for booking its flights.

Kayak, however, shows results from Priceline, Expedia, Travelocity and other third-party sites, and it refused to suppress those options for American flights.

In an Aug. 1 statement, Kayak said, "Kayak.com and SideStep.com are displaying schedules only (not prices) for American Airlines flights. Consumers are still able to compare AA itineraries along with those from hundreds of leading airlines, and if they wish to find the price or purchase an AA ticket, they can still do so by clicking on the Info link and we'll send them into the Orbitz booking path. We think this is a step backwards for consumers and we hope American changes its mind."

American noted that most third-party sites -- the exception is Priceline -- add fees of up to $12.99 for booking airline tickets. American, like most other airlines, does not charge a fee for booking on its site, and "we have a lowest-fare guarantee," a spokesman for the carrier said.

Kayak said it could not suppress results from one partner at the request of another. "We remain committed to providing a comprehensive and objective display to our users," the company said. Meanwhile, the flap has produced curious results for searches on Kayak for flights in American-dominated markets.

For example, a search for flights departing St. Louis on Aug. 15 and returning from Dallas/Fort Worth on Aug.22, a route on which American provides the only nonstop service, produced several pages of United, United-Delta and Continental one-stops, with a lowest fare of $212 on United. American's nonstops appeared on the 25th page of results, and the user had the option of clicking through to Orbitz (lowest total fare is $259.99) or its sister company, CheapTickets.com, (lowest total fare is $258.99). The lowest fare on aa.com was $216, while the lowest fares for American nonstops were $216 on Priceline and Expedia and $223 on Travelocity.