The videos have also been aired by some news channels, but the time, place and the identity of the persons involved are not known yet.
The PRO of Government Railway Police said police were examining CCTV footage from various stations in Mumbai.
"We haven't yet got the CCTV footage of the incident," he said, adding a DCP-rank officer would be conducting the probe.
The second clip shows the same youths being beaten up inside a local train. The videos, apparently shot by some commuter, went viral first on WhatsApp.
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Nobody has filed a complaint or informed the police about the incident, the PRO said, adding "we request the people to give any information they may have."
Lawyer and human rights activist Abha Singh termed the incident as serious and said the police should first register an FIR under section 324 (assault) and 341 (wrongful restraint) of the Indian Penal Code so a proper probe could start.
Former member of Divisional Railway Users Consultative Committee of Central Railway Rajiv Singal termed it a 'jungle- raj' and blamed the railway administration.
"When men can be beaten in full public view, we can easily understand where the safety of women passengers stands," he said.