Three men have been arrested on suspicion of murder after a woman was reported missing last week.
Lorraine Cox, 32 and from Exeter, Devon, was last seen in the early hours of 1 September in the city centre.
Police said they had been treating Ms Cox as a missing person but have now launched a murder inquiry following a “significant development”.
Three men aged, 22, 30 and 33 remain in police custody. Her next of kin have been informed.
Extensive searches are being carried out by specialist officers in and around Mary Arches Street in Exeter city centre, Devon and Cornwall police added.
“We would like to hear from anyone who believes they had seen or heard from Lorraine since 1 September as a matter of urgency,” Det Ch Insp Lee Nattrass said.
Anyone with information is urged to get in touch with the force quoting log 285 for 9 September.