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The 165-residence private cruise ship berthed at Port Chalmers about 7.30am yesterday.
The cruise ship - which is based in Miramar, Florida, and flies the flag of the Bahamas - has residents from more than 10 countries who live on board, some permanently.
Residents Douglas Schumann (69) and Sandi Davies (51), both of Naples, in the US, said they were enjoying their first visit to Dunedin although it was ''cold''.
The pair took the opportunity to see the locations The World visited by bicycle.
It was their second time in New Zealand and, despite the chilly weather, they were looking forward to snacking on ice cream.
''We seldom eat ice cream,'' Mr Schumann said.
''But we make an exception in New Zealand. It's so creamy.''
The pair was also looking forward to eating oysters and tackling the ''beautiful country'' by bicycle.
The biggest challenge in New Zealand was ''the hills'', Miss Davies said.
''But if they don't kill you, they make you stronger.''
The World sails for Stewart Island about 8pm today.