Two people, who did not want to be named, say a number of people have been pressurised to hand over thousands of pounds — sometimes at meetings in village halls.
One man, a farmer, was certain there was a pyramid scam operating in the area.
He said: "Quite a few of my friends are doing it and they have received their money but I'm worried that somebody will get caught."
He said the people running the scheme were urging people to hand over £3,000 with the promise they will get £24,000 back in return — but only if they recruited eight people to also donate £3,000.
The farmer, who has not joined the scheme, said contributors he knew were asked to take £24,000 to the people running the scheme in Bristol, where it was allegedly swapped for a different bundle of cash.
It has not been possible to verify these claims, although such schemes usually operate in a secretive way to avoid the attention of trading standards.
A Barnstaple woman said her boyfriend had been invited to a meeting to take part in a scheme, the details of which matched what the farmer told the Journal .
"A lot of his friends and quite a few people have invested in it. It just seems so dodgy and you have to go and invest money in cash."
She did not know who was organising the scheme but said it was being promoted by word of mouth.
She said the pyramid scheme was perhaps using a cloak of charitable giving, possibly by saying some of the cash was going to good causes.
Because it is impossible to sign up enough members to sustain the payments forever, it is a mathematical certainty that more people will lose money than make money.
Such scams, which have been found operating from Bristol and South Wales this year, are illegal.
DS Praveen Naidoo, from North Devon CID, said: "We have had third party reports of a chain gifting scheme operating in the South Molton area.
"We are liaising with the Office of Fair Trading, who are the lead co-ordinating body in this field, and Devon Trading Standards. Our advice is don't get involved and stay away from those schemes. If something sounds to good to be true, it generally is."
If you have been affected by a pyramid scam in North Devon or Torridge please email awilshaw@c-dm.co.uk or you can phone Trading Standards on 01392 381381.