"It is their desire that the inquest should not only be open, fair and transparent but that it should move swiftly to a conclusion," according to a letter from Jamie Lowther-Pinkerton, private secretary to the princes, which was read at the opening session.
Baroness Elizabeth Butler-Sloss, a retired senior judge and member of the House of Lords, presided at the preliminary hearings at the Royal Courts of Justice, which concentrated on procedural issues. She ruled that all sessions would be open to the public, and that the deaths of Diana and her friend Dodi Fayed would be examined together.
She also must decide whether to reach a verdict by herself or convene a jury.
Queen Elizabeth II sided with Fayed's father, Mohamed al Fayed, in urging that a jury — if called — should be made up of members of the general public. Because Diana was buried as a royal, normally an inquest jury would be made up of royal household members.
That would add to fuel to the conspiracy theorists' fire, reports CBS News correspondent Sheila MacVicar.
Fayed has accused the queen's husband, Prince Philip, of orchestrating a plot to murder Diana and Fayed. A police inquiry published last year concluded that there was no murder conspiracy, and that the deaths were accidental.
In a letter to the court, the queen's lawyer, Sir John Nutting, said that "in the particular circumstances of this case the public interest, it is submitted, would be best served by avoiding the course of (summoning) a 'royal' jury to avoid any appearance of bias in consideration of the issues which such an inquest would be bound to consider."
The full inquest, which was swiftly adjourned in 2004 shortly after it began, is expected to take place later this year, nearly a decade after the couple were killed in a car crash in a Paris tunnel. The inquest was put off until the French investigations were completed.
"The French procedure did not allow us to use their documentation until the main investigation was complete," Butler-Sloss said.
A two-year French investigation, a three-year Metropolitan Police inquiry and repeated legal action by al Fayed have delayed the inquests by nearly a decade.
Under British law, inquests are held when someone dies unexpectedly, violently or of unknown causes.
Diana's former private secretary, Patrick Jephson, said Monday that he hoped the inquest would put an end to conspiracy theories.
"At its best the inquest will show us that this sad matter is now settled and that we can concentrate on remembering the princess in an entirely positive light as Princes William and Harry obviously want us to," Jephson told British Broadcasting Corp. radio.
Al Fayed, who owns Harrods department store, pressed the British authorities to hold Monday's hearings in public and had threatened legal action if they did not.
Diana's sister Lady Sarah McCorquodale was in court, as was al Fayed.
The early hearings were originally going to be private, but Butler-Sloss decided otherwise, saying public interest in the case was overwhelming. Nearly 70 seats have been reserved for the media. An additional 50 seats have been set aside for the public, who will have to line up to see the early proceedings.
Late last year, a sweeping British police inquiry — which cost nearly $8 million — dismissed allegations that the princess was the victim of a murder conspiracy. The inquiry, headed by Lord Stevens, the former chief of the Metropolitan Police, said the chauffeur in the 1997 crash was drunk and driving at a high speed to elude pursuing photographers.
"On the evidence available there was no conspiracy to murder any occupants of that car. This was a tragic accident," he said.
Stevens' report largely confirmed previous findings by French investigators.
When the full inquest begins, Stevens' report "will assist in identifying the scope," according to the inquest's Web site, but Butler-Sloss will assess what evidence is relevant and which witnesses to call.
Diana, 36, and Fayed, 42, were killed along with chauffeur Henri Paul when their Mercedes crashed in the Pont d'Alma tunnel in on Aug. 31, 1997. The only survivor, bodyguard Trevor Rees-Jones, was badly hurt.
Al Fayed rejected Stevens' report.
"It's all baloney, it's all made up, as a cover-up, a hundred percent," Fayed said in an interview.
"For nine years I have fought against overwhelming odds and monstrous official obstructions. I will not stop now in my quest for the truth," he said in a statement.
"He believes that an establishment fix is already in, but he hopes that by good advocacy by his lawyers, he will be able to bring the truth out into the open," said his spokesman, Michael Cole Monday.
All the talk of conspiracies has served to obscure one very central fact, reports MacVicar: On the night she died, Diana was with Fayed's son, leaving a Fayed-owned hotel, with a Fayed driver, and a Fayed bodyguard, and with a plan made by the Fayed son.