Both incidents took place in Ormskirk Road, Pemberton. The first happened at 8.45pm on Wednesday, October 1, and the second two days later at about 8pm on October 3.
On both occasions, the 23-year-old victim was sexually assaulted as she walked along the main road near its junction with Enfield Street.

The woman says she has no idea who the man is and police say it may be that he has a fixation with her.
The offender is described as white, about 5ft 4in, about 18 or 19-years-old with cropped hair and a young-looking face.

He was wearing a Wigan Athletic FC top with dark trousers and spoke with a Wigan accent.
PC Lee Hughes, based at Pemberton Police Station, said: "We do not know why this man targeted this woman, but she is understandably distressed that in the space of just 48 hours she has been indecently assaulted by this man twice.

"These sort of offences put the victim through unimaginable distress so it is vital we catch this man and take him off the streets.
"Without wanting to cause any alarm, we would urge people – particularly young women – to not take shortcuts home, stick together and not walk alone where possible and keep to well-lit areas."

Anyone with information should call Pemberton police station on 0161 872 5050 or Crimestoppers anonymously on 0800 555 111.