After the wedding, the newlyweds will parade through the cobblestone streets of the capital's historic neighborhood in a horse-drawn carriage to the city's harbor. They will then take a boat to their reception at Drottningholm Palace, the official residence of King Carl XVI Gustaf and his wife, Queen Silvia.
The wedding is expected to draw several hundred guests, including royalty from Denmark, Norway, Greece and Japan. Britain's Prince Edward and the Countess of Wessex also plan to attend.
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Princess Madeleine, 30, is the youngest child of Sweden's king and queen. Also known as the Duchess of Halsingland and Gastrikland, she is the fourth in line of succession to the Swedish throne behind her sister, Crown Princess Victoria; a 1-year-old niece; and her brother, Prince Carl Philip.
O'Neill, the 38-year-old groom, was born and raised in London and educated in the United States. He has declined to use a royal title in Sweden because it would require him to become a citizen of the nation. He already holds dual American and British citizenship.
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The couple will continue to live in New York after their wedding. The princess works for the World Childhood Foundation, a charity her mother set up in 1999. O'Neill is a partner in Noster Capital, a hedge fund with offices in London and New York.