SEOUL – A U.S. lawsuit has been filed against Hyundai Motor Co and affiliate Kia Motors Corp, seeking $775 million in damages in one of the biggest known actions against the automakers since they admitted overstating the fuel economy of some their vehicles.

The South Korea carmakers conceded on Friday that they had overstated the fuel efficiency ratings on more than 1 million recently sold vehicles in the United States and Canada, and agreed to compensate owners for the additional fuel costs.

The lawsuit, which seeks class-action status, was filed in the U.S. District Court for Central California on behalf of 23 Hyundai and Kia car owners and challenges the automakers’ compensation plan.

Under the plan, customers will receive a debit card that will reimburse them for the difference in fuel economy, and an extra 15 percent to the amount will be added to acknowledge the inconvenience.

The lawsuit, which like a separate one filed in the Southern District of Ohio this week, is seeking further compensation for the reduced value of their vehicles.

Hyundai Motor was also sued in July by public interest group Consumer Watchdog for allegedly misleading consumers sensitive to high gas prices that its popular 2011 and 2012 Elantra model is more fuel efficient than it actually is.

A Hyundai Motor spokesman declined to comment on the lawsuits.

Moody’s Investors Service has estimated that the automakers’ compensation plan for fuel costs will cost them $100 million a year until the cars are scrapped but has not estimated potential legal costs.

Hyundai shares were down 1 percent on Thursday morning, and have lost 7 percent since rumours of lawsuits first emerged late last week. Kia’s stock fell 2.4 percent and has lost 5 percent since late last week.

The broader market was down 1.5 percent on Thursday.

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