A 27-year-old was attacked in the town's Doubledykes Road area in the early hours of Wednesday.
The same man is believed to have struck on the university campus at around 1am the next day.
An 18-year-old student was walking along a lane between the sports hall and the David Russell Apartments when she was grabbed by a man who indecently assaulted her before running off.
Police have warned females against walking alone at night in the town as they hunt for the suspect. Officers will also be patrolling the area at night.
The man is described as 5ft 8in to 5ft 10in tall. He wore a dark puffa-style jacket, tracksuit bottoms, a grey beanie hat and possibly gloves.
Detective Chief Inspector Pauline McCallum, of Police Scotland, said: "This type of incident is rare, but I would like to take this opportunity to remind the public to be aware of their personal safety, particularly if walking in a quiet area or after a night out.
"We have a description of a man who we would like to speak to in connection with our inquiries, and anyone with any information should contact police immediately."
A Police Scotland spokeswoman said: "In light of these two incidents there will be police foot patrols in place, particularly during the hours of darkness. Police are also advising people to be vigilant when walking home at night, and to walk in pairs where possible."