The astonishing claims are being investigated by the Mutual UFO Network (MUFON), which is the world's biggest organisation dedicated to UFO and alien research.
A report sent to MUFON said the incident happened at Landers, California, during a major UFO event.
The people reported seeing two light sources, that they believed could have been two objects, being tailed by the military aircraft.
The sighting happened at about 10pm local time on May 21, one day of the Contact in the Desert, three-day special event in Joshua Tree, California.
A night sky watch was carried out using night vision goggles with video camera after the conference.
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