Two women lost their handbags to doorstep callers on Friday.
A woman police described as “vulnerable” lost her handbag to a bogus caller who pretended to be from the “gas board” and said he could smell gas.
That incident happened in Millfield Road, Deeping St James, shortly before 6pm.
There was a previous incident involving an elderly woman in Vine Street, Billingborough, just before 5pm.
Police are warning residents to be on their guard when someone they don’t know comes to their door and to check the identities of callers.
A spokesman said: “A genuine caller will wait outside while you check by calling their organisation or by calling a family member or a neighbour.
“If you notice any suspicious persons contact Lincolnshire Police immediately on 101. If a bogus caller is at your door dial 999.
“Always say no to uninvited doorstep callers, close the door, contact the police.”
• Anyone who witnessed the incidents in Deeping St James or Billingborough can give information to the police on 101.