Mills, the 40-year-old former model whose marriage to the pop icon lasted less than four years, is representing herself in court after sacking her lawyers.

The case, expected to last five days, is being heard behind closed doors in the family division of London's High Court.

McCartney, one of the founders of the world's most famous pop group, is worth an estimated 825 million pounds ($1.6 billion).

Legal experts believe Mills is asking for up to 50 million pounds from McCartney, 65, and that he may be prepared to offer only half that sum.

The case could set an important precedent in measuring just how much a spouse can pitch for when short marriages fail -- McCartney's lawyers argue he made the bulk of his millions before he met Mills.

Mills, dressed in a grey suit and pink blouse, arrived first at the London court.

McCartney offered a cheery "Good Morning" to waiting reporters but remained tight-lipped when asked if there had been an out-of-court settlement.

Large "No Admittance" signs were fixed to the court doors and its windows were covered to ensure no one could look in.

The divorce, the most high-profile show business split since Tom Cruise and Nicole Kidman broke up, has turned into a battle for sympathy fought out under a media spotlight.

Mills' public relations adviser quit when Mills gave a string of tearful television interviews in which she said remorseless media coverage had driven her to the brink of suicide.

McCartney married Mills in 2002 four years after his first wife Linda died of cancer. Their daughter, Beatrice, is 4.

Their fate will be decided in an oak-paneled courtroom at the ornate Royal Courts of Justice, but the judge will hear the case in private and may reserve judgment until a later date.

Any settlement may also be subject to a gagging order to keep secret the details of the agreement.