The incidents all occurred between 7pm and 8.15pm on Tuesday (10/11) in Broadway and Wantage Road and involved four separate female victims.
All of the incidents have taken place along a popular route used by runners.
The first incident took place at 7pm on Wantage Road approaching the traffic lights by the UTC when a woman was inappropriately touched over her clothing.
Then at approximately 8pm, two further incidents were reported in Broadway, both opposite the fire station, when again, females were inappropriately touched.
A fourth incident occurred at around 8.15pm back in Wantage Road near to Didcot Hospital.
The offender in all four incidents is described as a black male with dark hair, aged in his mid-20s to early 30s and around 6ft tall.
He is described as having either a medium or athletic build and was wearing black clothing and a surgical face mask.
He was wearing a dark beanie-style hat and possibly a scarf.
One of the victims described the man as speaking with possibly a French accent with a deep voice and he was possibly wearing a gold earring.
The victims were all female, aged between 22 and 54-years-old.
Investigating officer PC Alyssa Weymouth, based at Didcot police station, said: “This appears to be a series of linked assaults on woman who were out running, and we have a very detailed description of a suspect.
“The descriptions from each of the victims is very similar, and so I am appealing to anybody who was in the Didcot area between 7pm and 8.30pm on Tuesday and believes they witnessed anything to please make contact with police.
“I would be particularly keen to hear from anybody who may have dash-cam or CCTV footage from the area to please check this and get in touch if it has captured anything that may assist this investigation.
“You can contact us by calling 101, quoting reference number 43200370048, make a report online or call the independent charity Crimestoppers 100% anonymously on 0800 555 111.
“You can also send dash-cam or CCTV footage or any information via our dedicated portal for this investigation at https://unitedkingdom1cpp-portal.digital-policing.co.uk/serip/appeal/sexual-assaults-didcot-10-11-2020.