24 May 2011 Last updated at 16:00 GMT The Queen welcomes President Obama to Buckingham PalaceThe Queen has greeted US President Barack Obama, and his wife Michelle, at the start of his first UK state visit.
The Obamas also met Prince Charles and the Duchess of Cornwall and spent 20 minutes with newlyweds the Duke and Duchess of Cambridge.
They have laid a wreath on the Tomb of the Unknown Warrior in Westminster Abbey and will attend a state banquet at Buckingham Palace.
It came after David Cameron and Mr Obama spoke of "essential" UK-US ties.
'Common interests'
In a joint article in the Times, Mr Obama and Mr Cameron said of their countries' relationship: "Ours is not just a special relationship, it is an essential relationship - for us and for the world.
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James Landale Deputy political editor, BBC News
Whenever a US president comes here there is always a slightly tortuous debate on whether or not the relationship is still special or not.
Both sides have decided the best way of avoiding that debate is to come up with a new wording entirely. They have a new adjective. It is now an essential relationship.
In a joint article for the Times newspaper, the prime minister and the president say the relationship between their countries was based originally on what they called emotional connections, sentiment and the ties of people and culture but now it thrives on common interests and shared values.
So what they are trying to focus on here now is more business-like pragmatism rather than any idea of appealing to the mythology of past historic links.
"When the United States and Britain stand together, our people and people around the world can become more secure and more prosperous.
"The reason it thrives is because it advances our common interests and shared values. It is a perfect alignment of what we both need and what we both believe."
The presidential pair's visit to Westminster Abbey included an impromptu meeting with choirboys, when Mr Obama was teased by his wife for his lack of singing talent.
"He insisted on speaking to each one of them and shaking their hands," the Dean, Dr John Hall said.
"He said that he liked to think he could sing and Mrs Obama said 'Well, he can't really, he can dance'."
Mr Obama briefly met the prime minister in Downing Street ahead of talks on Wednesday. They then left together for a surprise visit to the Globe Academy in Southwark, south London.
The leaders' talks are likely to focus on the Middle East and the ongoing conflict in Libya.
David and Samantha Cameron greet Barack and Michelle Obama
In their article, they also vowed not to abandon the protesters fighting for democracy in Arab countries, writing that they would "stand with those who want to bring light into dark, support those who seek freedom in place of repression, aid those laying the building blocks of democracy.
"We will not stand by as their aspirations get crushed in a hail of bombs, bullets and mortar fire.
"We are reluctant to use force, but when our interests and values come together, we know we have a responsibility to act."
BBC diplomatic correspondent Bridget Kendall said the two countries were anxious to play up their closeness.
"Security is the secret glue at the core of the special relationship, and that bond is being strengthened," our correspondent said.
"Behind the flags and formalities, be sure there are tensions, but in this era of tightened budgets and sudden crises, there's a new eagerness to work together."
Mr Obama arrived in the UK from the Republic of Ireland a day ahead of schedule on Monday, to avoid any disruption from a volcanic ash cloud.
After the president was welcomed by Prince Charles and his wife at the US ambassador's residence Winfield House in Regent's Park, his cavalcade made its way to Buckingham Palace where he joined the Queen.
They briefly met the Duke and Duchess of Cambridge before moving to the palace gardens where there was a ceremonial welcome, including a 41-gun salute.
There was an exchange of gifts, with the Obamas presenting the Queen with a collection of memorabilia and photographs from her parents' 1939 visit to the US.
They also received a selection of letters from the royal achives, between past US presidents and English monarchs.
When President Obama was shown letters and artefacts charting Britain's loss of the American colonies, he joked: "That was only a temporary blip in the relationship."
The royal newlyweds spent 20 minutes with the Obamas, but will not attend the state banquet
Michelle Obama was also given an antique brooch made of gold and red coral in the form of roses.
Number 10 barbecue
The Obamas are due to return to Buckingham Palace to meet Labour leader Ed Miliband.
In the evening there will be a state banquet at Buckingham Palace, where they will stay overnight.
Wednesday's itinerary will include talks with the prime minister before Mr Obama is joined by his wife and British and American military veterans for a barbecue at Number 10.
They will visit the Houses of Parliament and give a speech about US foreign policy to MPs in Westminster Hall, before a return banquet at Winfield House, where the Queen will formally say farewell.
The state visit to the UK is the 101st to be hosted by the Queen but only the third involving a US president in 100 years. The last US president to visit officially was George Bush in 2003.
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