The incidents happened on Wednesday 26 January 2022 at 11.10am in Nevill Park and 1pm near Broadwater Down.
In both incidents a man is reported to have been seen committing an indecent act. The suspect seen at Broadwater Down is described as being five feet and seven inches tall and wearing a black hat or hood, a black face mask and a green or khaki coat.
Inspector Ian Jones, of the Tunbridge Wells Community Safety Unit, said: ‘The two locations are fairly close and we suspect these offences may have been committed by the same man.
‘Investigators understand there were a number of people in both areas at the time and we would like to speak to anybody who witnessed a man acting suspiciously or indecently.’
Any witnesses are urged to contact Kent Police on 01622 604100, quoting reference 46/17359/22.
You can also contact Kent Crimestoppers anonymously on 0800 555111 or by using the online form on their website.