(Adds Queen's quotes, political comment, details)
By Anthony Deutsch and Sara Webb
AMSTERDAM, Jan 28 (Reuters) - Dutch Queen Beatrix, who turns 75 on Thursday, announced she was abdicating in favour of her son, Prince Willem-Alexander, telling her country it was time to hand the crown to the next generation after more than three decades on the throne.
Willem-Alexander, 45, who will be sworn in as king on April 30, is married to Princess Maxima, who comes from Argentina, and has three young children.
Decades of grooming for the throne involved shaking off his image as a beer-drinking fraternity boy whose blunt comments upset the press and politicians and did not fit the image of the Netherlands' low-key "bicycling monarchy".
Speaking calmly in a television broadcast, Beatrix, who once faced scandal over her father's involvement in a bribery case and whose middle son lies in a coma after a skiing accident, said she was stepping down because she felt Willem-Alexander was now ready to take her place on the throne.
"I am not stepping down because the tasks of the function are too great, but out of the conviction that the responsibilities of our country should be passed on to a new generation," she said.
"It is with the greatest confidence that on April 30 of this year I will pass on the kingship to my son, the Prince of Orange. He and Princess Maxima are entirely ready for their future tasks."
The decision appeared popular with ordinary Dutch people.
"She's been a strong, hard-working woman but it is good that she is now giving room to a younger generation," said Mandy, a 26-year-old who works as a secretary in Amsterdam.
A constitutional monarchy, the Netherlands has reduced the involvement of the Royal House in politics. The queen had taken part in forming government coalitions by appointing a mediator, a role that raised questions about undue influence on the democratic process and which was scrapped last year.
Sources close to the royal family said Beatrix did not want to go until she felt her son was ready and his children were old enough. She also wanted to ensure that anti-immigrant, eurosceptic politician Geert Wilders, of whom she disapproved, was in no danger of assuming real political influence.
She alluded in speeches to the need for tolerance and multi-culturalism, comments that were seen as criticisms of Wilders' anti-Islamic views - while Wilders criticised the queen, who has a penchant for huge hats, when she donned a Muslim headcovering on a trip to the Middle East.
Wilders' poor showing at the last election and loss of influence in politics, could well have contributed to her decision to abdicate.
FIRST KING IN A CENTURY
With Willem-Alexander on the throne, the Netherlands is likely to revive the debate about the role of the monarchy and the high cost of maintaining the royal household, particularly when ordinary Dutch people are having to deal with austerity measures.
"There is an ongoing discussion about the role of the royals in a modern society, and that discussion needs to continue," said Diederik Samsom, leader of the Labour Party, which is part of Prime Minister Mark Rutte's coalition government.
As queen, Beatrix often headed trade missions, most recently in Singapore, and was involved in promoting Dutch defence sales in the Middle East.
Beatrix, whose full name is Beatrix Wilhelmina Armgard, Princess of Oranje-Nassau, Princess of Lippe-Biesterfeld, has been on the throne since 1980, when she took over from Queen Juliana.
Dutch queens have made a tradition of stepping aside for the next generation over the last century. Queen Wilhemina handed over to her daughter in 1948 after half a century on the throne. Queen Juliana was in deteriorating mental health when she made way for the 42-year-old Beatrix in 1980.
Willem-Alexander, who majored in history and has specialised in water management, will become Willem IV -- the first Dutch king in more than a century.
The Dutch royal family is popular with the public, but like the British royals, it has not escaped scandal and controversy.
While she was still Crown Princess, Beatrix married former German diplomat Claus von Amsberg in 1966, and faced street protests over her choice of husband.
Von Amsberg had been a member of the Hitler Youth, albeit involuntarily, and as a teenager served briefly in the army of the country which occupied the Netherlands in World War Two.
Prince Claus later underwent treatment for severe depression between in the 1980s, blaming the difficulty he found in reconciling his private life with his responsibilities as a public figure.
In the 1970s, Beatrix intervened in the most serious crisis to hit the royal family since the war, threatening not to take up the throne should parliament decide to prosecute her father Prince Bernhard for taking bribes in the Lockheed scandal.
The queen was emotionally shaken when a man drove his car into a Queen's Day procession in 2009.
Willem-Alexander, the queen's eldest son, was once the darling of Dutch tabloids because of his love of fast cars, good-looking women, and partying.
He caused a stir when he married a commoner whose father was a civilian minister in Argentina's military dictatorship from 1976-1983. But his bride, Maxima Zorrigueta, quickly won over the public with her easy manner and quick mastery of Dutch, and often seems to be more popular than her husband.
Last year, the family faced tragedy when Willem-Alexander's younger brother, Prince Friso, had a skiing accident in Austria while going off-piste. He is still in a coma. (Reporting by Sara Webb and Anthony Deutsch; Additional reporting by Gilbert Kreijger; Editing by Robin Pomeroy and Giles Elgood)