The two bodies were found on the coastal path in Petitor Woods in Torquay.
David Cauldwell, 39, was reported missing from the town on 22 May.
A spokeswoman for Devon and Cornwall Police said there was no link between the two bodies found at the site.
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Officers first found the human remains - believed to have been there for a "considerable" time - at 20:45 BST on Tuesday. They discovered a second body, believed to be that of Mr Cauldwell, at about 08:10 BST on Wednesday.
Police said: "David Cauldwell's family have been informed of the developments but formal identification has not yet taken place.
"The area has been cordoned off and a full investigation is being carried out to establish the circumstances of both deaths. Support will be offered to families and friends when the identities have been confirmed."
It is understood police believe they know the identity of the human remains due to an item discovered where they were found.
Mr Cauldwell was last seen leaving the Artful Dodger pub in Teignmouth Road, Torquay, at about midnight on 21 May.
Police searching for a missing man have discovered what they believe to be his body and a second set of human remains nearby.