The incidents took place at the Sketty Hall side of the park, which is near Bishop Gore comprehensive school.
The unidentified man reportedly ran off after exposing himself, before police arrived.
Police say their enquiries are ongoing in efforts to identify the man
A spokesperson for South Wales Police said: “We have received two reports in recent weeks of indecent exposure involving a man at the Sketty Hall side of Singleton Park. The most recent report was received on Saturday, March 22.
“Enquiries are currently ongoing to identify the man, who has departed the scene prior to officers’ arrival. There will be an increased policing presence in the area while this investigation is taking place. Anyone who witnesses such behaviour should report it to 101. Always call 999 in an emergency.”
