Saudi Crown Prince Sultan bin Abdulaziz al Saud has died, Saudi TV says.
The crown prince was King Abdullah's half-brother and first in line to the Saudi throne. He was also minister of defence and aviation.
He was in his eighties and was diagnosed with colon cancer in 2004. He is thought to have died at a New York hospital.
Prince Sultan had been on a visit to the US for medical tests, and he had an operation in New York in July.
The royal court confirmed the death in a statement carried by SPA, the state news agency:
"With deep sorrow and sadness the Custodian of the Two Holy Mosques King Abdullah bin Abdulaziz mourns the death of his brother and his Crown Prince Sultan... who died at dawn this morning Saturday outside the kingdom following an illness."
US Secretary of State Hillary Clinton paid tribute to the crown prince, saying Washington's ties with Saudi Arabia were "strong and enduring".
"The Crown Prince was a strong leader and a good friend to the United States over many years, as well as a tireless champion for his country," Mrs Clinton said during a visit to Tajikistan.
Crown Prince Sultan was a member of the most powerful family group in Saudi Arabia, the Sudairi Seven, and one of the sons of the country's founder, King Abdulaziz, known as Ibn Saud.
The Sudairi Seven are the sons of Ibn Saud's most influential wife, Hassa bint Ahmad al-Sudairi.
The oldest of the seven was King Fahd, who died in 2005 - to be succeeded by a half-brother, the current King Abdullah.
Prince Sultan's first appointment was as governor of Riyadh and he became minister of defence and aviation in 1963.
He oversaw extraordinary expenditure on modernising the armed forces - with multi-billion dollar deals making Saudi Arabia one of the world's biggest arms spenders.
Prince Sultan was also involved in the setting up and development of the national airline, Saudia.
He was one of the strongest supporters of forging close ties with the US, which faced its biggest challenge after 9/11.
His son, Prince Bandar, was instrumental in this as the kingdom's Washington ambassador for more than 20 years.
But BBC Middle East analyst Sebastian Usher says that, with the current generation of Saudi leaders now in their seventies or eighties, there is no clear idea yet of who will take over among Ibn Saud's legion of grandsons when they have died out.
Next in line
Prince Sultan's most likely successor as the next in line to the Saudi throne is Prince Nayef, 78, also a half-brother of King Abdullah and one of the Sudairi Seven.
He has been the interior minister, in charge of the security forces, since 1975. In contrast to King Abdullah, who is seen as a cautious reformer, Prince Nayef is believed to be closer to conservative Wahhabi clerics.
Earlier this year, as part of a package of reforms to see off unrest spreading from other Arab countries, the king announced an extra 60,000 posts to be created within the security forces.
In 2009, after Prince Sultan fell ill, King Abdullah named Nayef as his second deputy prime minister, traditionally the post of the second in line to the throne.
However, the king - who is 87- has also established a succession council, made up of his brothers and nephews.
It is expected to meet for the first time to determine who will be named as the next in line to the Saudi throne.