A man is understood to have carried out multiple acts of indecency in front of groups of women and girls.
Both incidents reportedly took place on two separate trams on Saturday, May 7.
The first incident is understood to have taken place in front of two women on the tram at Cator Lane in Beeston, at around 11.30pm.
The same man then reportedly exposed himself to two girls, aged 16 and 17, at around 11.40pm on a separate tram from Toton Lane to Hucknall.
He is understood to have then left the tram at High Road in Beeston, at midnight.
Police have released images of a man they would like to speak to in relation to the incidents.
PC Michael Appleton, of Nottinghamshire Police, said: “This was a disturbing sequence of events that understandably left the victims in this case very upset.
“Nottinghamshire Police treats all offences of this nature extremely seriously and our investigation continues.
“We have released CCTV images of a man that we’d like to speak to about what happened, so we’d urge anyone who recognises him to get in touch with us immediately.
“Anyone with information is asked to contact Nottinghamshire Police on 101, quoting incident 90 of 9 May 2022.”