Click on photos below for gallery of Dutch royals' tour.
Willem-Alexander and Maxima, who started their tour on the Dutch Caribbean island of St. Maarten, were greeted by cheers and applause from crowds who had gathered to welcome the couple.
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Maxima, 42, looked particularly touched by the warm welcome, as she was presented with a beautiful bouquet and tenderly touched the cheek of one child.
The royal couple were all smiles as they looked out to the sea of welcome banners and waving orange flags – the national colour of the Netherlands – and leant in to shake hands and high-five the young children.
Fashionable Maxima was the picture of elegance in a pastel-coloured dress that fell just above the knee. The mother-of-three protected her face from the blazing sun with a peach, wide-brimmed hat and wore a matching shawl to complete her graceful look.
The Dutch monarchs then paid a visit to the Milton Peters College where they were greeted by cheering schoolchildren dressed immaturely in checked uniform. One young girl in particular was clearly elated to see the Dutch queen, as she reached out and hugged the elegant royal around the waist.
During their visit of St. Maarten, Willem-Alexander and Maxima also enjoyed a walk through the capital's Frontstreet, looking out to the clear, azure sea. The couple visited the Oranje School where they were met by the sound of ringing bells and also listened to a beautiful church choir singing in the Methodist church.
Earlier in the day, Willem-Alexander and Maxima met with governor Eugene Holiday and other members of state and posed on the government balcony for photographs. They were also welcomed with an official opening ceremony by military guards.
The Dutch royals were making their first official visit to the Netherlands' Caribbean territories since becoming reigning monarchs in April, after Willem-Alexander's mother, the former Queen Beatrix, abdicated.
As part of their official tour around the Dutch Caribbean islands, Willem-Alexander and Maxima are also expected to visit Saba, St. Eustatius, Bonaire, Curacao and Aruba. The monarchs will end their tour on 21 November.
The Dutch colonized the islands in the 17th century, and they once formed part of the Netherlands Antilles.