One pilot is said to have seen 'two square lights' that were 'large and orange'.
Two flying instructors and their students were flying over Gloucestershire when all four pilots spotted the lights on Thursday, between 8.15pm and 8.45pm.
Both small aeroplanes tried to track down the objects but could not reach them.
A spokesman for Air Midwest - a flying school and aviation services company based at the airport in Bobbington, south Staffordshire, said: "At approximately 8.15pm, one of our aircraft was tracking south towards Gloucester at 7,000ft after leaving the Birmingham air traffic zone.
"At the same time one of our other aircraft was also tracking south towards Gloucester at 4,000ft when both aircraft observed one red and one orange light in the the sky, south of Gloucester.
"Our aircraft approached the lights on an interception track but were unable to gain on the objects as they appeared to move further south of Gloucester as our aircraft approached. We were unable to identify the lights."
One pilot was the school's chief flight instructor. He is a long haul airline pilot with 40 years of flying experience and 22,000 flying hours under his belt.
The other instructor has 10 years flying experience and 2,000 flying hours, and also flies for a UK airline.
Both students were also fully qualified pilots who were taking part in night navigation training.
The two pilots, flying in a Grob G115 and PA-28 Warrior, spoke to air traffic control and each other about what they had witnessed.
The flying school has made its own enquiries as to what the objects were, but so far have found no answers.
It is the first time that the flying school has encountered a 'UFO' event, said director Tim Brannon.
"There were reports all over about this UFO," said Tim.
"In this game you see things from time to time of what we would call UFOs. It was the first one for us. We just so happened to have our chief flying instructor and another instructor who spotted it.
"What our pilots saw didn't have the signature of any known aircraft that we know of."
One of the instructors filed a report on what they witnessed.
The pilot said: "I observed, initially, two large square orange lights, one on top of each other, but slightly off set. However there was a gap in height between them.
"The top object was constantly orange. The lower one occasionally flickered white, but for the majority of the time it was orange. In addition to that, on two occasions I observed five orange lights but that was momentarily.
"I initially observed them when leaving the Birmingham control zone. I thought they were just south of Gloucester and definitely a lot higher then us. We then climbed 5,000ft and they seemed level at that height and stationary.
"As we approached Gloucester, it became apparent that they were now further south, maybe beyond Bristol even as far as Weston-super-Mare, but directly south of Gloucester airport.
"On our return leg up to our home base (at Halfpenny Green Airport), we climbed 7,000ft by Worcester and commenced a turn to observe the lights. At this point they seemed lower than us in the same place and stationary.
"I have no idea what these objects were”
The flying school spokesman added: "That is all we can say on the matter.
"Night glow balloons? But unlikely as these do not move very fast at all.
"So what were they?
"We have no idea. An interesting event."