Operators of rented mopeds suffered two serious accidents this week on the same stretch of Seaview avenue near Lola’s Restaurant in Oak Bluffs. In both accidents, moped operators lost control, crossed the center line and crashed into oncoming auto traffic.

On Wednesday, James Allen, 59, and Kathleen Sztaba, 48, suffered injuries serious enough for doctors at the Martha’s Vineyard Hospital to order them airlifted to Massachusetts General Hospital. Both Mr. Allen, who suffered a fractured and dislocated shoulder, and Ms. Sztaba, who had head injuries, are now listed in good condition at the Boston hospital.

The two were sharing a moped, heading toward Edgartown, shortly before 1 p.m. when it crossed the double yellow line and collided with two oncoming cars, a Volvo driven by Dolph Vanderpol and a Saturn driven by Sarah Earley. Drivers of the cars were uninjured, but the vehicles sustained damage according to police, who issued no citations in the accident.

The police report did not indicate from which dealership the couple had rented their moped.

Last Saturday afternoon, in another moped accident in the same area, 48-year-old George Croteau also lost control, veered over the center line and collided with a GMC Yukon driven by Edward Herczeg.

Mr. Croteau was taken by ambulance to the Martha’s Vineyard Hospital and treated for orthopedic injuries before being released the same day. Police said Mr. Croteau had rented his moped from Ride-On Mopeds on Lake avenue in Oak Bluffs. No citations were issued by police.

This area of Oak Bluffs has been a particularly bad patch for moped riders this year. In an almost carbon-copy accident, Kate Dunnet Miller of Virginia lost control of her moped near the sea wall and crashed into an oncoming car. She died of head injuries, becoming the fourth person killed in a moped accident on the Island since 1996.