Kate Middleton is reported to be responding well to treatment for acute morning sickness after a second day in hospital.
Prince William was at his pregnant wife's bedside and two top royal doctors were seen arriving to join the medical team, The Daily Mail reported.
Sources said the Duchess of Cambridge was bearing up well, but severe vomiting may last for much of her pregnancy after she developed the rare illness hyperemesis gravidarum.
Her illness has led to speculation she may be expecting two babies, with experts saying the condition was slightly more common with twins.
Kate, 30, who is less than 12 weeks pregnant, has been on a drip to restore lost nutrients since being driven to the King Edward VII Hospital in central London by her husband yesterday.
Earlier today (local time) the Duke had arrived looking hunched and tense with his head bowed.
Officials said Kate was expected to spend the next few days in hospital, and needed a period of rest to recover from the rare illness that had left her weak and tired.
Today the two royal gynaecologists treating Kate were seen going to the hospital where she is being cared for.
Consultant Alan Farthing is overseeing the birth and Marcus Setchell, who spent two decades as the Queen's surgeon, is also helping Kate through her illness.
Kate's mother Carole Middleton is planning to visit.
The duchess is possibly only two months pregnant, and her condition makes it almost impossible to eat or drink.
Meanwhile, The Guardian reported "massed ranks of the international media" were waiting outside the hospital.
However there were few facts for presenters filling airtime on television channels across the globe.
International interest in the royal baby, who will be third in line to the throne, was intense, an early indication of the level of media interest the couple will endure throughout the pregnancy and beyond.
The Duke and Duchess did not want to make the pregnancy announcement until Christmas but were forced to make a statement because of Kate's hospital admission. The Queen was reportedly only told yesterday.
Bookmaker Paddy Power cut the odds on the Duchess having twins from 50/1 to 8/1, after what the company described as a "rush of money" on two babies. Odds on triplets came down from 1000/1 to 100/1, The Telegraph said.
Victoria was now the most heavily backed name for the new baby, dropping from 20/1 to 8/1, while Elizabeth, Diana and Charles were also among the favourites.