It happened between 4.40pm and 5.15pm on Thursday, May 16.
Two 13-year-old girls were travelling from Monument towards Heworth and were touched inappropriately over their clothing by another passenger.
Police have a description of a man who was on the Metro at the time and may be able to assist them.
He is said to be white, aged 30 to 40-years-old, of large build, with short brown hair with bits of grey in it and a short beard. He was wearing a chequered shirt, had a bag over his shoulder and was wearing glasses. Police have an image from CCTV cameras that will be released if he does not come forward.
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A Nexus spokesman said: “We urge anyone with information about this offence to get in contact with the police so that the culprit can be traced as soon as possible. The safety and security of customers is our top priority.
“While offending of this nature is rare on Metro when it does occur we always work closely with the police.
“We have record levels of staffing on the system, supported by the police, and that is backed up by a network of more than 600 CCTV cameras.”
The man, or anyone who recognises him, is encouraged to contact police on 101 or via the website or email at [email protected] quoting log 951 16/05/19 or Crimestoppers on 0800 555 111.