The royal couple have confirmed the news that they are expecting another baby.
Prince William said he and Kate are "thrilled" to be expecting their second child.
The Duke of Cambridge visited the University of Oxford to open it's new China Centre today without the Duchess.
It was revealed this morning that she is pregnant with a younger brother or sister for Prince George - and suffering from acute morning sickness which meant she could not attend the event.
The Prince was all smiles as he arrived in Oxford this afternoon, where he was met by school children, students and staff.
At the end of his visit he said a few words about Kate's condition: "She's feeling ok thanks," the Prince said. "It's been a tricky few days, a week or so.
"But basically we are thrilled, it's great mews, early days. We are hoping things just settle down and she feels better...
He added: "I'm going to go and look after her now."
William suggested that Kate may be able to resume royal duties in a fortnight.
When a well-wisher sympathised with Kate's condition and said they wished she could have attended, the Duke replied: "I know, she wishes she could be here - a few weeks' time."
Prime Minister David Cameron was among the first to offer his congratulations to the couple, saying: "Many congratulations to the Duke and Duchess of Cambridge. I'm delighted by the happy news that they're expecting another baby."
The announcement that the couple are expecting their second child comes two months after Prince George turned one.