Smiling under the gaze of the world's media, Spanish King Juan Carlos's daughter Cristina faced a judge on Saturday as a corruption suspect, in an unprecedented blow to the royals.

A judge started questioning her over accusations that she was complicit in tax-dodging and laundering allegedly embezzled money -- claims that have plunged the monarchy into crisis.

The blonde 48-year-old princess stepped out of a dark car and walked into a court in Palma on the holiday island of Majorca, nodding to television crews, photographers and reporters crowded near the door.

Dressed in a white shirt and black jacket, the princess appeared relaxed as she headed into the closed-door hearing with a judge who suspects her of tax fraud and money-laundering.

"She is calm," one of her lawyers, Jesus Maria Silva, told reporters.

Scores of pro-republican protesters rallied nearby, held back by police barriers.

They brandished red, yellow and purple republican flags and banners with slogans such as "Royal blood = unreal justice" or "Heads of state by the ballot, not the cradle".

The hearing follows more than two years of mounting anger against the elite in a Spain battered by recession.

"It seems the privileges they have aren't enough for them -- they have to do something that really annoys the people," said Mateo Castellanos, 61, who travelled hundreds of miles from the mainland to protest.

"A large part of the country is suffering hardship and a lot people don't have enough to feed their children," he said.

The spectacle unfolded on a warm winter's day under sunny skies, on an island where for decades Cristina's family sunbathed and sailed yachts in carefree summers.

Now the island is the centre of an embarrassing scandal that has turned much of the public against the royals and raised doubts over the very future of the monarchy.

Minutes after Cristina's arrival, investigating judge Jose Castro began questioning her in a courtroom overlooked by a portrait of her own father, Juan Carlos, 76.

- From untouchable to fraud suspect -

Long thought untouchable as a royal, Cristina finds herself in the centre of the scandal, accused of being complicit in allegedly fraudulent business dealings of her husband, who is also under investigation.

Neither Cristina nor her husband, former Olympic handball player Inaki Urdangarin, have been formally charged with any crime and both deny wrongdoing.

Castro has spent more than two years investigating allegations that Urdangarin and a former business partner embezzled six million euros ($8 million) in public funds via a charitable foundation.

Cristina was a member of the foundation's board and with her husband jointly owned another company, Aizoon, which investigators suspect served as a front for laundering embezzled money.

State prosecutors say there is no case to answer against Cristina but the judge has admitted suits brought by pressure groups.

"This is an unprecedented case," said Virginia Lopez, a lawyer for one of the plaintiffs, the far-right pressure group Manos Limpias. "I hope justice will be done."

It is the first time a direct member of the royal family has ever gone to court as a suspect.

Juan Carlos won widespread respect for helping steer Spain to democracy after the death of the dictator Francisco Franco in 1975.

But the royals' popularity has plunged since the case against Urdangarin opened three years ago.

The king's woes were worsened by a luxury elephant-hunting trip he made to Africa in 2012 as his subjects suffered in a recession.

These scandals and the sight of the king looking frail on crutches in his rare public appearances have raised debate about the future of his reign.

A recent poll showed 62 percent of Spaniards in favour of his abdication. Support for the monarchy in general fell to just under half.