The first incident happened overnight from Thursday into Friday, when 24 sheep were stolen from a field at Thurston Mains Farm, near Dunbar.
In the next theft, which happened overnight from Friday into Saturday, 15 sheep were stolen from a field to the north of Nunraw Abbey, near Garvald.
The value of the sheep is estimated around £2700. They all belonged to the same farmer.
A Lothian and Borders Police spokesman said: “The thief would have had to transport the sheep in a vehicle, and we are appealing to anyone who was in the areas where the thefts took place, who noticed any suspicious overnight activity, to contact police.
“Similarly, anyone who has been offered the sheep for sale, or who has any other information that can help us trace those responsible, should also get in touch.”
Anyone with any information should contact Lothian and Borders Police on 0131 311 3131, or Crimestoppers in confidence and complete anonymity on 0800 555 111.