In 1568, a cluster of provinces in the northwest corner of Europe revolted against King Philip II of Spain. They won, eventually, with the support of their overlord, Prince William of Orange.

Their descendants -- now citizens of the Netherlands -- never forgot the favor, and today they will honor a new queen and heir to William's house: Beatrix Wilhelmina Armgard, Princess of the Netherlands, Princess of Orange-Nassaau, Princess of Lippe-Biesterfeld.

The Netherlands is an odd place to find royalty still being celebrated. Fiercely democratic, highly socialized and determinedly informal, the Dutch would seem an unlikely subject of the formal, traditional ways of courts.

But then, even the Dutch find moments of grandeur difficult to part with. Besides, their royal house has learned to temper its style to Dutch tastes.

Democratically inclined and constitutionally limited, the Dutch monarchy keeps to modest proportions, with fewer trappings and a much smaller household -- 250 or so -- than England's royal clan. There is no showy changing of the guard for the bearers of this kingly crest.

For the past 32 years, the Netherlands' royal house has been ruled by Juliana, a grandmotherly figure of a queen who turns 71 today. She has earned the affections of the people by her gentle manner, her regal if slightly eccentric style, her deep sense of duty and informal actions, such as writing her own speeches and riding a bicycle.

The cloud of scandal has hung over her husband, Prince Bernhard, who, in 1976, was charged by a government commission with misusing his position to solicit large sums of money from the Lockheed Aircraft Corp. and subsequently was forced from his government and military positions. But Bernhard's problems seemed only to draw more sympathy for the queen and boost her own popularity among the 14 million Dutch, Juliana's official reason for stepping down was age. Her mother, the austere Wilhelmina, gave up the throne at age 68 after a half-century reign.

The question here is what kind of queen will Beatrix be. The consensus appears to be: a different queen than her mother.

Beatrix, 42, has not appeared often in public on official occasions, causing many Dutch to feel they do not really know her. Her soft, round face carries a ready smile. At the same time, there is an arstocratic air to her manner and speech that some say indicates her aloofness.

Information about the royal family is strictly controlled and there is little one can glean from public sources about the real Beatrix. The court's official biography says, "The princess is deeply interested in sculpture, painting, dramatic art and ballet, and regularly attends exhibitions, plays and ballet performances. She likes to talk to the artists and performers." She is also described as being keen on sports, especially riding, skiing, swiming and tennis.

Beatrix is widely regarded as more intelligent and more practical than her idealistic mother.She is also said to be more headstrong, an impression that stems in large part from her insistence in 1966 on marrying Claus von Amsberg, a West German diplomat whose background as a member of the Hitler Youth raised more than eybrows in the Netherlands.

Beatrix threatened to go on a hunger strike unless her parents approved the marriage, and once they did, she refused to get married in the quiet of The Hague, pressing instead for a formal wedding in Amsterdam.

Such open displays of stubbornness will not work for her once she is on the throne. "The danger is that Beatrix will try to exert her will too much," said one source close to the royal family. "She must not overplay her hand. She must not appear to want to dominate. The basic formula of the House of Orange has been not to stand above the people, but to live with them."

The Dutch monarch's powers are extremely limited by the Dutch Constitution. They consist chiefly of selecting the person who forms a new government after each national election.

This can be a delicate process, since the country's system of proportional representation ensures that any government will be a coalition. There are 13 parties currently represented in Parliament.

In general, the Dutch monarch is expected to take social initiatives but not to mix in politics. The monarch is protected from political responsibility by the Constitution, which says, "The king can do no wrong. The ministers are responsible."

One Western diplomat observed, "Beatrix will be more successful the less political she is."

Recently, Beatrix showed herself skillful in fielding sensitive political questions. At a luncheon with Dutch editors, she was asked to comment on the plight of Amsterdam's "squatters" -- part of an influx of youth from the Netherlands' rural areas -- who have complained about overcrowding and whom police fear will try to disrupt the investiture ceremony.

Beatrix called the squatters' increasingly militant actions an emotional reaction to a real problem.

Prince Claus, 53 a handsome and quiet-spoken man, is said by court observers to be a good counselor to Beatrix. After an upsetting introduction, he has become widely popular in the Netherlands for his energetic interest in environmental and Third World issues. He has also learned to speak Dutch well.

The Netherlands that Beatrix inherits is quite different from the one her mother saw when she first took the throne in 1948. The country then was rebuilding from World War II. Growth followed, spurred by the discovery in the early 1960s of extensive natural gas fields. Wealth from these financed expansion of a welfare state with benefits exceeding those of all but the Scandinavian countries.

But economic prosperity is no longer a matter of course in the Netherlands.

White tourist posters still show the romantic version of the Netherlands -- a land of quiet, solid prosperity filled with dikes, windmills and wooden shoes -- government planners worry about the future of the factories, shipyards, refineris and gas fields that have become the mainstays of the country.

Amid signs of economic fatigue and stagnation, the center-right Dutch government has tried to cut back on public expenditures, which now account for nearly half the gross national product. The public expenditures also support the world's highest minimum wage of $913 per month.

Social tensions have become increasingly apparent. A series of union actions in the past year spoiled the once cooperative relationship between labor and management.

In foreign policy, too, there has been a shift away from unquestioned adherence to the Atlantic alliance and European solidarity and toward a return to the Netherlands' pre-World War II neutralist stance. These developments have caused some to question whether a monarchy is needed in today's Netherlands. For one thing, it is expensive to maintain. The queen receives an annual allowance of $2.6 million, while the princess receives $600,000 and the two husbands receive about $500,000 each.

Most Dutch maintain that they are fundamentally republican. But when all is said and done, 80 to 90 percent say they prefer to hold on to their monarchy for the sake of tradition and stability and to do business with foreign governments that like the idea of dealing with a royal family.

A handful of Dutch parliamentarians have announced that they will not attend the royal investiture, saying they refuse to swear the traditional oath to the new queen to uphold the inviolability and rights of the crown.

From time to time, the Dutch government has considered limiting the number in the royal house who are actually in line of succession to the throne so that the government would not be responsible for what all royal family members do and say.

The issue came up again earlier this year. But Juliana insisted that there be no discrimination among her children, and Prime Minister Andries Van Agt dropped the matter.

Beatrix has three sons and her sister, Margriet, has four, all of whom are now in the line of succession. Musing on this next generation, Jeske Heldring, director of the Netherlands Society for International Affairs, says he is convinced that the boys will be the undoing of the Dutch monarchy.

"They will fill the gossip columns, they will want jobs but won't be able to get real ones," Heldring said recently. "Boys, of course, will be boys, but too many princes will, I predict, spoil the royal house."