Police Scotland state that 16 valuable fish have vanished from the pond beside a house at Grahamsfield, Kirkpatrick Fleming.
The theft occurred sometime overnight Sunday May 31 and Monday June 1.
Officers say the haul included orange goldfish, black and orange koi and large orange carp, which could have a combined value of around £400.
The latest incident follows a similar theft from a garden at near-by Springfield on Tuesday April 21.
On that occasion in the region of 15 koi carp, valued at around £500, were stolen from a pond at a house in the village’s Newton Square.
Police believe that theft took place sometime between 5.30 am and 6.30 pm on that day.
A spokeswoman for Gretna Police, Constable Michelle Hamill, said: “This is a very unusual type of theft for our area, and certainly to have two similar thefts, only a few miles apart and in such a short timescale, does add to the theory that they may be linked.
“We are, however, keeping an open mind and would ask anyone who may have any information, which may assist in these enquiries, to get in touch with me through telephone number 101.”