I think that you refer to the NATO AWACS planes normally stationed in Europe. They are some of the last built 707-300 type planes with P&W PT3D engines, I think it's TF-30 in military designation.
For some reason they carry a civil registration in Luxembourg which has no air force. Don't know why. But at least that way it was avoided to fight over which air force they should belong to.
Crews are mixed from all NATO countries.
Don't know either where they are normally based, they probably never saw Luxembourg.
I heard that some of them will be on duty in the US while many USAF AWACS planes are at war.
Regards, Preben Norholm
Always keep your number of landings equal to your number of take-offs