Police have launched an investigation after the discoveries by the farmer in two different fields.
And they say one of the sheep appears to have been attacked by some sort of animal, whilst all that remained of the other was the fleece and two legs.
The sheep are valued at around £80 each.
Constable Cameron Pagan said: “Investigations have started after police were alerted by the farmer. At this stage it seems one the of the sheep has been attacked by some sort of animal, either before or after it died, as there is evidence of this. However, the second sheep appears to have been skinned in some way, and all that is left is the fleece and two legs.
“We want to hear from anyone who may have been in the Holywood area late on Monday night through to early on Tuesday morning.”
Anyone who may have seen or heard anything suspicious is asked to call us on the 101 number, quoting PDG00064101118.