Denmark's Crown Prince Frederik and his Australian-born wife Crown Princess Mary were greeted by cheering crowds as they inspected seaside sculptures and enjoyed pedal-powered smoothies.

Hundreds of well-wishers on Sunday gathered along the coastal walk to Sydney's famous Bondi Beach where the royal couple took in the annual Sculptures by the Sea exhibition -- an event they visited when first dating 11 years ago.

Two young schoolchildren presented the crown princess with flowers and she joked about the heat as she stopped to admire a baby and chat with another woman about what to do when you're expecting twins.

"Synchronisation and organisation", the princess replied.

It is the couple's first visit to Australia since Princess Mary gave birth to twins Prince Vincent and Princess Jospehine, who are now 10 months old.

The pair first met in Sydney during the 2000 Olympics and New South Wales Premier Barry O'Farrell said many in the city felt a special affection for their "fairytale" romance.

From Bondi they travelled to Circular Quay, on the city's iconic harbour, to launch an urban sustainability exhibition, where they were again greeted by fans waving Danish flags.

They won a round of applause after jumping on energy-generating bicycles to churn out pedal-powered fruit smoothies.

A barbecue business lunch on the harbour's Garden Island and talks with Governor-General Quentin Bryce, Queen Elizabeth II's representative in Australia were also on the agenda for Sunday.

The royal couple is leading a business delegation investigating green energy, sustainable living and food technologies in a bid to enhance trade and investment ties.