The Duke and Duchess of Cambridge are expecting their second baby.

The Queen and members of both William and Kate's families are "delighted" with the news, Kensington Palace said.

Kate is said to be suffering from acute morning sickness, as she did with her first pregnancy, and is being treated by doctors at Kensington Palace. She is no longer joining her husband on a planned engagement in Oxford today.

Prime Minister David Cameron offered his congratulations to the couple today, saying: "Many congratulations to the Duke and Duchess of Cambridge. I'm delighted by the happy news that they're expecting another baby."

Kate was due to join William in formally opening Oxford University's £21 million centre dedicated to the study of China. He will still attend, as planned, Kensington Palace said.

The announcement that the couple are expecting their second child comes two months after Prince George turned one.

The third-in-line to the throne was born on July 22 last year to a worldwide fanfare.

Kate suffered with hyperemesis gravidarum with her last pregnancy and is suffering from the very acute morning sickness again, meaning she may need extra hydration, medication and nutrients.

The couple's second child will become fourth in line to the throne, shifting Prince Harry further down the line of succession.

The Duchess of Cambridge's announcement will throw into doubt whether she will be able to attend her first solo overseas tour, set to take place in Malta later this month.

It is understood that Kate's pregnancy has not passed the 12-week stage - a similar position to when she was struck by the illness when in the early stages of her first pregnancy.

A Kensington Palace spokesman said the Duchess's attendance at future events would be decided on a "case by case" basis.

Kate is scheduled to be among the guests at the opening ceremony of the Invictus Games in London on Wednesday evening along with William, Harry and the Prince of Wales and Duchess of Cornwall.

The following day she is due to attend a solemn Drumhead service at Lee Valley Athletics Centre with the Duke and Harry, and later with William to watch Invictus competitors taking part in matches and heats.

The Duchess is due to make her first official solo overseas tour for two days in two weeks' time, from September 20-21.

A spokesman said: "We will be planning this on a case by case basis - it's too early to talk about Malta and Invictus."

Scotland's First Minister Alex Salmond said: "This is very happy news for any couple, and on behalf of the people of Scotland, I am delighted to send our best wishes to the Countess and our hearty congratulations to the royal couple."

The Duchess is known in Scotland as the Countess of Strathearn.