Police Scotland are looking to trace the men discovered by a member of staff at Hetland Hall Hotel in Carrutherstown in the early hours of Monday morning.
PC Louise Bryden at Annan Police Station said: “We are unsure how the two men gained access to the hotel.
“However, it seems they were not in there for any legitimate purpose.”
At about 5 am on Monday a member of staff at the hotel discovered two men in the premises.
When challenged, the two men made the excuse that they were looking for accommodation, before making a quick exit.
After they had left it was discovered that a small amount of cash and a bottle of alcohol had been stolen.
The first man is described as being 5’7″ tall, in his 30s, of slim build and wearing a grey jumper. He spoke with an English accent.
The second man is described as 5’5″ tall, in his 50s, of stout build and with a scruffy and unshaven appearance, and wearing blue shorts and a blue baseball cap.
PC Bryden said: “We would ask anyone who may have been in the vicinity of the hotel in the early hours to get in touch if they can help us identify these two men.”
Police can be contacted at Annan Police Station using the non-emergency 101 number.