Illawarra residents have been targeted by scam callers claiming to represent Australian authorities.

Figtree pensioner Val Fell and Dapto mother Sheridan Field received phone calls last week from men with foreign accents, accusing them of dubious tax crimes and threatening arrest.

In Mrs Field's case, the caller, with an Indian accent, introduced himself as Jason O'Connor and told her she was the subject of a lawsuit "concerning tax evasion".

"The police officer from the local police department will approach you at your place and issue a warrant for your arrest," the man said, in a message on Mrs Field's answering machine. Mrs Field returned his call, using the number 02 6152 8648, but quickly recognised the scam.

"I said, 'This sounds like bulls..t' - then he got cranky at me," she said.

"He said, 'This call is being recorded for training purposes' and, 'I don't appreciate you talking like that'.

"I could see how some elderly people could [believe it]."

Mrs Fell had two messages left on her answering machine by a man claiming to be from the "Commonwealth Directors of Public Prosecution".

He encouraged her to return his call at 03 6107 9616 before "your warrant for arrest is sent for execution".

Mrs Fell did not return the call.

"I'm an elderly lady but I've given lectures on internet safety and I can cope with this kind of thing," she said.

Fair Trading has warned residents about the scam calls. The ATO does not cold-call about debts and does not threaten jail or arrest - it sends a letter or an SMS to remind people payment is due.

An elderly Bulli resident told the Advertiser about a scam call she received. She said a man claimed he was from the "accident report department of the RTA" said an accident had been reported from her address.

"I said my car hadn't been in an accident and hung up."

Information: scamwatch.gov.au or 1300 795 995