Two women were robbed by men posing as water board officials.
Police are not sure whether the crimes are connected. Two men called on an 87-year-old woman in Bicester Road, Kidlington. One kept her talking while the other stole cash.
Det Con Mark Rudman, of Kidlington CID, said: "There are callous criminals around who think nothing of stealing from vulnerable old people."
Any other sightings of these men should be reported to Kidlington CID on 01865 846972.
Two men also stole cash from an 86-year-old woman in Deddington. The men are believed to be in their 20s and one wore a grey pullover.
Call Banbury CID on 01295 754575 if you can help.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article