One of the planes remained grounded in Oslo on Monday due to problems with the oxygen supply to the cockpit, according to Norwegian Air spokeswoman Aasa Larsson.
"Technicians are working to fix the problem," she told Reuters.
A valve had been repaired on the second plane on Sunday, and the delayed flight eventually left Oslo for New York.
"It has now landed there," Larsson said.
Technical problems have forced Norwegian Air to ground the planes several times in recent weeks, due to problems with brakes, hydraulic pumps and power issues.
The Dreamliner was expected to be a game-changer for the aviation industry as its use of lighter materials and new engines promised 20 percent savings in fuel consumption.
But the programme has been troubled by delays in getting the planes into service and setbacks including the temporary grounding of all planes because of overheating batteries.
(Reporting by Joachim Dagenborg; writing by Terje Solsvik; editing by Keiron Henderson)