In the first incident in Livingston, West Lothian, a 21-year-old woman was attacked in the back garden of a property in Scott Brae at around 5.20am on Tuesday April 8.
In a subsequent incident around a month later, a 27-year-old woman was assaulted at an address in Orchard Place in the early hours of Wednesday May 7.
Detectives said they are keen to speak to a man they believe will be able to help with their inquiries.
He is described as being white, around 5ft 8in to 5ft 10in with dark hair and he wearing a grey hooded top.
Information also suggests that he has worn a pair of dark-coloured Adidas Adipure Essence trainers.
He may have had a scratch on his back and an injury to his pinkie finger in recent months.
Police Scotland urged members of the public to come forward if they recognise the description.
Detective Superintendent Pat Campbell said: "We ask our communities to get in touch if they recognise the description of the man or remember seeing any suspicious activity in either Scott Brae or Orchard Place during the times of each attack.
"If you believe you know this person or have information that can help police to trace him then please contact police immediately."
Police Scotland can be contacted on 101.