STATUE: This grainy image of the disc thrower statue which used to stand in Rock Park has been taken from an old glass negative kept at The Athenaeum in Barnstaple Library.
Graham Avery and Len Shaddick said the sandstone statues were distinctive features in the park when they were teenagers.
Both men now want to solve the mystery of what happened to the statues — and are appealing for readers to come forward with information and pictures.
And there is even a rumour the statues are still buried in the park and could be rediscovered, perhaps by a Time Team-style dig.
Graham said: "There were two statues, made of sandstone, standing on a large plinth. One was like a Roman character, throwing a disc. The other was a woman without any clothes on.
"I used to pass them on my way to school and one day they just weren't there. We all want to know where they have gone." Len, who has a slightly-blurred old photograph of the disc-thrower, said: "I can personally only remember the one statue, the disc thrower.
"But when I mentioned it to a friend, he also knew exactly what I was talking about.
"He said 'that's Mr Rock, the man who donated the park'."
Although Len cannot remember the dates when the statue stood, he is sure it was no longer standing when he returned from national service in 1957.
The men have heard rumours that the statue was bulldozed into a nearby pond, which has since been filled in.
Graham has frequently looked over the area, near to the Skate Park, for clues as to the statues' whereabouts, but to no avail.
Sandi Whildash-Daws at the North Devon Atheneum found a photograph dating back to 1950 which showed the disc thrower statue on a plinth next to the pond.
She also located a photograph of a Grecian lady statue, probably dating back to 1897, which stood next to a mound. This may have been the female statue Graham remembers.
Denise Teague, manager at the Barnstaple Heritage Centre, said: "It is definite the disc thrower was there - although I am not sure about the other statue.
"However, it is believed it might still be buried in the park."
Denise explained that in the 1940s, the area - which is now the sports ground - was turned into a rubbish tip where up to six feet of rubbish was collected.
"There is the possibility the statue was simply pushed down and buried under the rubbish.
"When the sports ground began to be built, the area was landscaped and the statue was left underneath."
Len said: "I try my best to keep up the heritage of this town, because it is fading away.
"Anything we can do to keep it alive is worth it - I'm sure this statue is one of those things a lot of people will remember."
● If you have any photos, memories or information about the statues phone 01271 347 440 or e-mail scockroft@c-dm.co.uk or leave a comment below.