Prince William smiled with relief as he left his pregnant wife in the care of two top royal doctors and issued a statement last night saying Kate is 'continuing to feel better'.
Quoting sources, The daily Mail said the Duchess, 30, is responding well to treatment.
The couple also said they are 'immensely grateful for the good wishes they have received' as the Duke left the King Edward VII hospital in clear good spirits after spending hours at his wife's bedside.
A St James's Palace spokesman said on Tuesday night: "The Duchess of Cambridge is continuing to feel better. She and the Duke are immensely grateful for the good wishes they have received.
She will remain in hospital at present and will continue to be treated for Hyperemesis Gravidarum."
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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 on Tuesday.
MailOnline sources on Wednesday confirmed the Duchess is bearing up well - but her symptoms of severe vomiting may last for much of her pregnancy.
She is likely to be taking anti-sickness tablets after developing the rare illness Hyperemesis Gravidarum that
affects one in 50 women.