According to this following article, the couple will be seperated for one year followed by a divorce:
Danish Royal's Marriage to British Commoner Breaks Up
Prince Joachim, second in line to the Danish throne, is to divorce his British wife, a spokesman for the royal family said today.
In a statement read by Ove Ullerup, the Royal family’s Lord Chamberlain, Queen Margrethe and her husband Prince Henrik “deeply regretted” the couple’s decision, but added they would give their full support to their son and daughter-in-law.
Ullerup said Joachim and Princess Alexandra would continue their official duties during the divorce.
The princess will keep her royal title during the one year separation period. If the divorce is completed, then it will be the queen’s decision whether to let Alexandra keep her royal title.
The announcement marks the first time since 1846 that the royal family, Europe’s oldest ruling monarchy, has had a member divorce.
The monarchy was founded by the Viking Gorm the Old, who died in 958.
Joachim, 35, married Hong Kong-born British commoner, 40-year-old Alexandra Manley, in November 1995 at the Frederiksborg Castle in Hilleroed.
The couple have two sons, Prince Nikolai, five, and Prince Felix, two.
In the past months, there have been rumours in the Danish media that the couple were living separate lives.
Joachim is the younger brother to the heir to Denmark’s throne, Crown Prince Frederik, who in May married Australian-born Crown Princess Mary.
After their wedding, the enormously popular Princess Alexandra, captured Danes’ hearts and admiration by giving a speech in fluent Danish.
Alexandra spends considerable time in the public eye, serving as the patron of 21 groups, including the Danish Association for the Blind, a marine life museum, a girls’ choir and a shelter for homeless and abused women with children. She is also the president of Unicef Denmark.
While Alexandra carried out official duties, Joachim was dubbed “the party prince” because he spent more time attending football matches, racing vintage cars and rock concerts.
The couple met in January 1994 in Hong Kong, where the prince was working for a Danish shipping company.
After marrying into Europe’s oldest ruling monarchy, Alexandra gave up her professional life as a mutual fund manager and dropped her British citizenship for a Danish passport.
Known as an elegant dresser, Alexandra speaks German and French. She studied economics in Hong Kong, London and Vienna.