More than 70 antitrust class actions have been filed against Korean Air Lines Co. in the wake of its agreement to pay a $300 million fine to the U.S. Department of Justice and plead guilty to fixing prices on international passenger and cargo air fares.

The fine, levied in August, is the first in the federal government’s two-year investigation into whether some of the world’s major airlines set up illegal cartels with each other in order to charge artificially high fuel surcharges to passengers and purchasers of air freight shipping.