They did not reveal whether the baby would be a boy or a girl.
The couple already have two children: George, 4, and Charlotte, 2. George is third in line to become king.
"As with her two previous pregnancies, the Duchess is suffering from hyperemesis gravidarum," a condition that brings excessive nausea and vomiting, the palace said.
She had cancelled an engagement at a children's centre in London on Monday, and was being cared for at Kensington Palace.
The younger royal family were in Germany in July, and have other foreign trips planned. It is unclear whether they will go ahead.
Social media users welcomed the news, with many tweeters wishing Kate the best as she faces hyperemesis gravidarum for a third time.
The royal announcement came just days after the royal family marked a more sombre occasion: the 20th anniversary of the death of Diana, the Princess of Wales.
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The couple already have two children: George, 4, and Charlotte, 2. George is third in line to become king.
"As with her two previous pregnancies, the Duchess is suffering from hyperemesis gravidarum," a condition that brings excessive nausea and vomiting, the palace said.
She had cancelled an engagement at a children's centre in London on Monday, and was being cared for at Kensington Palace.
The younger royal family were in Germany in July, and have other foreign trips planned. It is unclear whether they will go ahead.
Social media users welcomed the news, with many tweeters wishing Kate the best as she faces hyperemesis gravidarum for a third time.
The royal announcement came just days after the royal family marked a more sombre occasion: the 20th anniversary of the death of Diana, the Princess of Wales.
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