People are warned to be on their guard after at least 18 homes were targeted by a bogus caller in one day.
In each case the potential victim received a call from a person calling themselves Max Morris, who spoke with an American accent and said he was calling from Coopers Law Firm.
He then the firm was involved in a case going to court against or involving them and that they had to call back on a number given.
Most of the messages, which were made to homes in the Eastbourne area yesterday, were left on answer phones.
None of those targeted by the caller rang back and although many dialled 1471, the number was withheld.
A Sussex Police spokesman said; "We urge anyone hearing about these calls to pass the message on to any friends and relatives who may not be aware of this particular type of targeted fraud, to prevent any vulnerable friends or family members from becoming victims."
The motive for the calls is not clear, although it is suspected that some type of fraud was intended.
Anyone receiving such calls should contact Sussex Police on 101 or email firstname.lastname@example.org.