Some U.S. Navy pilots reported seeing unidentified flying objects while training over the East Coast in 2014 and 2015 in interviews with The New York Times. According to The Times, multiple Navy pilots spotted "strange objects" with "no visible engine" reaching 30,000 feet and going hypersonic speeds.

The Times report includes a minute-long video of two encounters Navy pilots allegedly had with unexplained aerial phenomena. In the videos, which include visual radar and voice recordings, pilots cannot distinguish what is seen on their radar screens. At one point one of the pilots says in amazement, "Look at that thing. It's rotating."

"These things would be out there all day," Lt. Ryan Graves, an F/A-18 Super Hornet pilot and 10-year Navy veteran, told The Times. "Keeping an aircraft in the air requires a significant amount of energy. With the speeds we observed, 12 hours in the air is 11 hours longer than we'd expect."

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Josh Gradisher, a Navy spokesperson, told the newspaper that the U.S. Navy doesn't have all the answers for the observations made by Lt. Graves and others.

"There were a number of different reports," Gradisher said. Some cases could have been commercial drones, he said, but in other cases "we don't know who's doing this, we don't have enough data to track this. So the intent of the message to the fleet is to provide updated guidance on reporting procedures for suspected intrusions into our airspace."

According to The Times, the Navy recently set out new classified guidance for how to report "unexplained aerial phenomena."

According to the report, the pilots who reported the aerial phenomena "speculated that the objects were part of some classified and extremely advanced drone program." In another instance, one pilot told Lt. Graves that he "almost hit one of those things" and that he described it as looking "like a sphere encasing a cube."

Lt. Graves and his fellow pilots told the newspaper that "the video showed objects accelerating to hypersonic speed, making sudden stops and instantaneous turns — something beyond the physical limits of a human crew."

Video captured by U.S. Navy pilots offers an inside look at a secretive government program that investigated unidentified flying objects, or UFOs. CBS News

CBS News has previously reported on a little-known Pentagon program with a budget of about $22 million, one that investigated unidentified flying objects before the Defense Department ended it in 2012. While the Defense Department says it ended the Advanced Aviation Threat Identification Program in 2012 over funding issues, a Pentagon spokeswoman said: "The DoD takes seriously all threats and potential threats to our people, our assets, and our mission and takes action whenever credible information is developed."

Last year, two airline pilots claimed an unidentified flying object flew over top their planes at an altitude of 30,000 feet in Arizona. According to the radio logs, two separate pilots of a Learjet operated by Phoenix Air and an American Airlines flight saw the object flying in the opposite direction of their planes.