Prince William has said he and the Duchess of Cambridge are 'immensely thrilled' to be expecting a second baby.
Kate is suffering from 'very acute morning sickness' - as she did in the first weeks of her pregnancy with Prince George.
Speaking at a visit to Oxford University the Duke of Cambridge said it had been a 'tricky few days' but was 'great news'.
The couple's second baby will become fourth in line to the throne, behind Prince George, who celebrated his first birthday in June. The new royal baby will shunt Prince Harry into fifth position in the royal lineage.
Prince William was speaking after he opened a £21m China study centre at Oxford University.
The Duchess had been due to accompany him on the visit, but her morning sickness meant she stayed home.
The Duchess's first pregnancy was revealed when she was just a few weeks pregnant with Prince George after she was admitted to hospital suffering from severe morning sickness in December 2012.
Hyperemesis gravidarum causes severe vomiting and can lead to dehydration, weight loss and a build-up of toxins in the blood or urine, called ketosis. At its worst, women can be affected throughout their pregnancy and may need frequent hospital treatment. Last time cynics were swift to point out that after her brief stay in hospital Kate was able to return to her official engagements.
The Duke told a wellwisher who sympathised with Kate's trying first trimester that she may be over the worst of the acute morning sickness in 'a few weeks' time'.
Kensington Palace said the Duchess's attendance at future events would be decided on a 'case-by-case' basis.