The 30-year-old royal - who is expecting her first child with husband Prince William - is currently being treated in London's King Edward VII Hospital and officials say she is responding well to treatment.
A palace spokesperson said: "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."
Yesterday (04.12.12), Catherine - who is also known by her maiden name of Kate Middleton - was visited by William and her parents, Carole and Michael Middleton.
After spending six hours by his wife's bedside, William, 30, emerged smiling, indicating Catherine was doing much better.
The duchess has also received a get well soon message from brother-in-law Prince Harry, who is currently fighting on the frontline in Afghanistan.
The thrilled uncle-to-be was given news of his sister-in-law's pregnancy on Monday and contacted Catherine at her hospital to say he was thinking of her.
A source told The Sun newspaper: "Harry jumped for joy when he heard the news that Kate is expecting. He's really looking forward to coming back and can't wait to be an uncle."