When King Abdullah invites foreign leaders into his office in his opulent Jeddah palace, he sits by a painting which shows a supplicant presenting a petition to the elderly monarch's father – the man who gave his name to modern Saudi Arabia.
As the dignitaries glance from father to son, their gaze comes to rest on the 84-year-old ruler seated before them in the wood-panelled and marble room, wrapped in his chestnut robe. They can be forgiven for thinking: who's next? Because uncertainty is looming over the literally tottering House of Saud. Saudi Arabia's geriatric leaders are at each others' throats, circling like caged animals waiting for the first to die.
King Abdullah is supposed to be succeeded by his half brother and arch-rival, Crown Prince Sultan, who is also in his 80s. However, since the crown prince returned from medical treatment in Geneva at the beginning of May, there have been rumours that he is dying of cancer. The possibility that he could die before the king has aroused fears that the bitter feud between the two rival wings of the Saud family could be reignited in a power struggle in which dozens of contenders could come forward to claim the throne. The king has 60 siblings.
Abdullah, who became king three years ago, is heralded by some as a reforming monarch. They point to measures taken to ensure a smooth succession and the stability of the kingdom which is the world's biggest oil producer, not to mention the home of Mecca, where political turmoil can have a global impact.
After succeeding the equally geriatric King Fahd, who died after a long illness, Abdullah issued a decree providing for an "allegiance council" of sons and grandsons of the country's founder, Abdul al Aziz al Saud, to decide on the future successions once Sultan became king.
The fresh concerns about the health of Prince Sultan, who had previously had intestinal surgery, could put paid to the king's carefully laid plans.
For someone rumoured to be at death's door, the crown prince appeared in rude health at a meeting on Sunday with the UN secretary-general, Ban Ki-moon. Participants at the talks in Jeddah's Khaldia palace said that he looked fit and healthy, and that his voice was booming. "His voice was louder than anyone else's," said one.
King Abdullah himself also appears robust for a man of his age, with his goatee beard as suspiciously dark as ever. He impressed the UN delegation with his passionate advocacy, particularly on his pet project of an inter-faith dialogue between Muslims, Christians and Jews, during talks lasting more than an hour on Saturday evening.
Saudi Arabia, with its tradition of polygamy, is no ordinary monarchy where the succession passes to the eldest son. The Saud family boasts an estimated 7,000 princes. But it is split between the al-Sudairy wing and the more liberal al-Faisals.
Abdullah was one of the 25 half brothers of the late king Fahd. Until he produced his succession blueprint in 2006 – to avoid the feuding that led to him becoming king – there was no such formal procedure.
If all goes to plan, on Abdullah's death the throne would return to the al-Sudairy branch and to the powerful "Sudairy seven", as the six full brothers of the late king Fahd are known. In addition to Crown Prince Sultan, the longtime Defence Minister, they also include Prince Naif, the Interior Minister, and the Governor of Riyadh, Prince Salman, who both have claims on the monarchy.
The only member of the al-Faisal branch with a prominent position in government today is Prince Saud, the Foreign Minister, who is in his 70s. But he is also said to be ailing. He abruptly cancelled a dinner appointment with Mr Ban on Saturday evening, although he greeted him at the airport and personally drove the UN secretary general to the meeting with the king, in which he took a prominent part. King Abdullah spoke in Arabic, although he broke off from time to time to correct the translator's English.
At another meeting on Sunday, Prince Saud appeared to be in some pain, although he was smiling and joking with his foreign guests.
Analysts agree that if Crown Prince Sultan dies before the king, it is "anybody's guess" as to who will succeed when the monarch passes away, although Prince Naif is seen as the front-runner. It is thought that the allegiance council will have to be convened. At the end of Fahd's reign, there was much speculation that the Saudis needed to skip a generation to reinvigorate the leadership, but they carried on in time-honoured fashion by passing the torch to one of the brothers. It may take another decade before the grandsons of the founder get their chance.
Among them are the sons of Prince Naif and Prince Salman. Another name mentioned is that of Prince Alwaleed bin Talal, the supremely wealthy Saudi financier who is another grandson of the founder. Although the prince is very liberal, "that amount of money can buy political loyalty," said a Western diplomat.
King Abdullah's death, when it comes, will be a milestone for Saudi Arabia. Although the house of Saud is widely considered by Saudis to be morally bankrupt, and criticised outside the country for its espousal of the radical wahhabi brand of Islam, King Abdullah is credited with setting out on the road of reform.
He has quashed the al-Qa'ida insurgency and pursued education as a route to counter Islamist violence. Prosperity has returned to the kingdom, where more than 50 per cent of the population is aged under 15, thanks to the rise in oil prices which sustain the system of patronage and stifle initiatives for change. But political parties remain banned.
He has reached out to fellow Muslims as he seeks to end Saudi Arabia's isolation, which worsened after the 11 September 2001 terror attacks in which 15 of the 19 suicide attackers were Saudi nationals. The country was already at loggerheads with the administration of the US President, George Bush – its otherwise staunch ally – who accused it of being soft on terrorism after the Khobar Towers bombing on a foreigners' compound in 1998.
But relations with Britain and the US remain tense over the fallout from the BAE corruption case and its continuing ramifications.
Saudi Arabia has been active in the search for a political solution in Lebanon – the Druze leader, Walid Jumblatt, was in Jeddah to see the king last weekend – and was instrumental in obtaining a UN-brokered ceasefire in Somalia. The king expects to host the signing ceremony this month and could hold the key to persuading other Muslim states to take part in a "stabilisation force" underpinning the Somali agreement.
In addition to pushing for the creation of a Palestinian state according to the timeline set by President Bush, the Saudis have also reached out to the UN by providing $500m (£255m) to the World Food Programme to help the UN agency meet its commitments to the world's poorest at a time of rocketing food prices. Mr Ban was treated like royalty during his visit at the weekend, from the royal 777 jet – where a birthday cake awaited the South Korean UN chief – to the red-carpet welcome.
"They want to help. They don't want to be blamed," Mr Ban said on the plane that whisked him back to London on Sunday after he learned that the Saudis were boosting production in the hope of bringing down the surging oil price that is in turn affecting global food prices. "They were in shock after 11 September," said one diplomat. "Now they're on a charm offensive, it's plain to see."
Whether that offensive will outlast the reign of Abdullah remains to be seen. Crown Prince Sultan is expected to brake reform. Prince Naif is also a conservative who initially refused to admit that Saudis were involved in the 11 September bombings.
But as conservatives they could be more in tune with the mood of the country, particularly in the rural areas. The Saudi analyst Mai Yamani explained in her book Changed Identities that a return to Islamic ways – albeit a more flexible interpretation of Islam – is the most acceptable solution for most Saudis.
Can the House of Saud survive? Western analysts believe so. The family has consolidated their rule through tribe, region and religion. "For the time being, they are secure. They have co-opted the resentment, and the jihadists over-reached themselves," said Gerd Nonneman, of the think-tank Chatham House, who points out that the main threat to the regime comes not from the liberal side but from the Islamists.
But change in Saudi Arabia moves at a snail's pace. A Pakistani in his 40s who has just returned to Saudi Arabia, where he spent his childhood, received an email from a friend who explained how things had improved over the years. "Remember when you were a child? You could only see the eyes of women through slits in the veil. Now you can see the whole face," she wrote.
Princes seeking power: contenders for the Saudi throne
Crown Prince Sultan
Long-serving defence minister and workaholic with a reputation as "the epitomy of corruption". His lavish spending is legendary: he doles out money at banquets in keeping with tribal custom. A conservative expected to put a brake on Abdullah's timid reforms assuming he becomes king. As defence minister he commands the armed forces. A pro-American whose son, Prince Bandar, is a former US envoy.
Prince Mohammed bin Naif
Son of Prince Naif, the interior minister, who has delegated much responsibility to Prince Mohammed. He is assistant minister for security affairs, but his brief appears to be broader because of family influence.
Interior Minister (below) and clearly the heir in waiting in case the Crown Prince dies. Hardliner with tough reputation as head of security and counter-terrorism. Also responsible for charity organisations which gave money to tsunami victims but which have also been accused of funnelling funds to Islamic radicals. A supporter of the religious police who nonetheless created surprise by speaking out against the separation of men from women.
Foreign minister (below) since 1975 who brought the Saudi peace plan (of then Crown Prince Abdullah) for the Middle East to the world's attention. Very bright but his chances in succession stakes have been clouded by illness. Member of the well-educated and liberal al-Faisal branch of the Saud family which is respected both among Arabs and in the West. Strong advocate of political and social reform from within.
Reform-minded prince from al-Faisal branch who has encouraged the media to act as a public watchdog. Former intelligence chief who became ambassador to Britain then US envoy. Marginalised himself on his sudden return to Saudi Arabia in 2005 from Washington, and now heads King Faisal foundation. In recent weeks his public profile has exploded. Would be the West's favourite to become king.
Sultan bin Salman
Son of the governor of Riyadh, Prince Salman, who is one of the "Sudairy Seven" and thus a possible contender for the throne. The first Arab and Muslim astronaut in space in 1995, and a national hero. "Looking at [Earth] from up here, the troubles all over the world and not just in the Middle East look very strange as you see the boundaries and the border lines disappearing," he said from space. His words boosted US-Saudi friendship.