Saudi Arabia, ever keen to preserve its stability, is likely to act quickly and appoint Prince Nayef bin Abdul Aziz, the obvious choice, as the new heir of the thrown, analysts said.
"There is only one candidate who has all the possibilities of becoming crown prince: Prince Nayef," the interior minister and King Abdullah's half-brother, Abdul Aziz al-Sager, chairman of the Gulf Research Centre, told AFP.
"It is the first time in the history of Saudi Arabia that the crown prince disappears and it falls on the king to propose a new one," said Sager.
Saudi Crown Prince Sultan bin Abdul Aziz, aged 80, died on Saturday in a New York hospital and will be buried in Riyadh on Tuesday.
Prince Sultan passed away while the monarch himself, 87, remains in hospital in Riyadh, a week after he had an operation on his back.
Sager said the decision on who will be the next crown prince is likely to come swiftly: "perhaps even before the repatriation of the remains of Prince Sultan."
"The regional and international environment requires a quick endorsement of the king's decision," said the analyst, referring in particular to the unrest in neighbouring Yemen, a major concern for the Saudi leadership.
The situation in Syria and tense ties with Iran, accused of attempting to assassinate the Saudi ambassador to Washington, are another source of anxiety for the ultra-conservative Gulf monarchy.
Traditionally, successions in the oil-rich kingdom have always been held without apparent conflict among members of the royal family.
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Since the death in 1953 of King Abdel Aziz, who founded Saudi Arabia in 1932, five of his sons have ascended to the throne.
Most power transfers have been smooth, except that of 1964, when king Saud was forced to abdicate in favour of his brother and then crown prince, Faisal.
Khaled Dakhil, a political science professor at the King Saud University, also said the "most prominent candidate to inherit the throne is Prince Nayef."
"The appointment of Prince Nayef as second vice-president of the cabinet is a strong indication that he will be made crown prince," he added.
Prince Nayef, 78, was named second deputy premier in March 2009, filling a potential void in the succession lineup.
"The choice should not take long, if it hasn't been made already, because the members of prince Sultan's family knew his health was very bad."
For the first time in the in the kingdom's history that choice, in principle, must be endorsed by a small Al-Saud board, which was established following a reform of the system of succession in 2006.
Anwar Eshki, director of the Saudi-based Middle East Institute for Strategic Studies, said the board will make the decision taking into consideration experience, whereas before the sole criteria was age.
Prince Nayef, who liked to say he was a soldier at the service of the country, boasts plenty of experience, particularly as the head of the powerful ministry of interior.
Widely viewed as a conservative, he has led the campaign against Islamist militants in the kingdom after it witnessed a wave of deadly attacks by Al-Qaeda between 2003 and 2006.
More recently, Prince Nayef has mobilized his servicemen to prevent the "Arab Spring" from spreading to the regional power-house, and publically thanked Saudis for ignoring calls for demonstrations.