Several sheep were left badly mauled after being attacked by dogs in Copthorne.
The attacks happened on Tuesday January 13 and Monday January 19 at Woodmans Farm, Copthorne.
One of the sheep has had to be destroyed due to the severity of its injuries.
Police are now warning dog owners to keep their pets under proper control at all times.
A spokesman said a large, dark-coloured dog was believed to have been involved, as clumps of its fur were left behind.
Farmers have the right to shoot dead any dog posing an immediate threat to their livestock if it seems reasonable to do so.
Under the Dogs (Protection of Livestock) Act it is a criminal offence to let a dog worry sheep and owners/handlers risk a fine of up to £1,000 if they do so.
Anyone who has information about either sheep worrying incident is asked to email email@example.com or phone 101, quoting serial 881 of 19/1.