Several people have reported seeing glowing orange balls hovering and then disappearing at speed — and they are demanding an explanation.
One man was so baffled he got in touch with the Ministry of Defence (MoD), and he has received a response from one of its directors of staff.
The Post has received phone calls about the bizarre sightings after an article on Tuesday, which reported Mumbles man Colin Hopkins seeing a 10ft glowing ball drifting over Swansea Bay last Friday evening.
A stunned David Williams, of Briton Ferry, saw the article and went to speak to Mr Hopkins before contacting the Post.
He is adamant he saw three orange lights when he was driving home from Spar, in Briton Ferry — but this was on Saturday evening, not Friday.
The 42-year-old remains absolutely flabbergasted.
"I was driving home, and on my right there was an orange sphere," he said.
"It was pulsating, about 100ft up. I had no idea what it was.
"I got out of the car, and asked a young couple walking along the road if they saw it as well.
"The young man was taking video footage with his camera.
"Then two elderly gentlemen came along with a camera and started taking pictures.
"One of them said he'd seen it hovering above his garden.
"The orange glow had white light emanating from it," added the father- of-two.
"Then it accelerated upwards. I was about to drive off when one of the men said: 'There's another one coming'.
"It was amazing. It went to the exact place as the first one, and started rising.
"Then a third one came and followed the same trajectory. They had incredible acceleration."
Mr Williams then went home, got his camera out as the lights were still visible and contacted the MoD.
Mumbles man Mr Hopkins said two people had been in touch with him about similar versions of what he saw.
Explanations could be floating Chinese- style lanterns, or disco lights.
Another man, David Humphrey, of Neath, has also got in touch with the Post.
He was sitting with his wife at home on Saturday night when a glowing light, then another, drifted across the sky about 500 metres in the air.
He filmed what he saw, and took photos.
"There was absolutely no sound," he said. My neighbour has seen the footage — he couldn't believe it," said Mr Humphrey.
Military aircraft have been flying in South Wales as part of a Nato exercise, but RAF community relations officer Peter Sinclair said: "It's highly unlikely to have been any activities to do with these exercises."
The MoD added: "There is no evidence that airspace has been compromised by hostile or unauthorised air activity."