Police are advising people to be on their guard after a fresh spate of investment and romance scams have proved costly for unsuspecting victims duped out of large amounts of money.

A number of serious fraud complaints have sparked police investigations after New Zealanders transferred money into offshore accounts in sophisticated scams.

The latest to cause alarm include an investment scam where people are cold-called from Hong Kong or China and offered shares in well-known companies offering large returns.

There is also a romance scam where victims meet a person through an online dating site and unknowingly transfer stolen funds into offshore bank accounts.

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On each occasion the offenders are from overseas countries and once they receive the first payment of money they continue to pressure victims to transfer larger sums of money at short notice.

Both scams are lasting for months.

Wellington CIB Constable Ross Barnett said people should be extremely cautious about buying shares overseas or transferring money on other people's behalf and giving money to any one they have not met in person.

The best thing people could do was hang up or seek expert advice before any money changed hands.

Other scams include winning an overseas lottery but needing to pay money to receive the prize, people impersonating legitimate businesses but siphoning the money to a different bank account and pretending to be a law enforcement agency and demanding money for illegal material that has been downloaded on to the victim's computer.