That is important for Britain, for which the $20bn Al-Yamamah arms-for- oil package is the defence industry's biggest weapons contract.
Yet stability in Saudi Arabia is important for other reasons: as the Gulf war showed, the kingdom is a vital restraint on the territorial ambitions of regional powers such as Iraq and Iran. Serious and persistent unrest in a country that is custodian of the Islamic shrines of Mecca and Medina would unsettle the region and might set back the peace process with Israel. Not least significant, Saudi Arabia is the location of a quarter of the world's oil reserves.
Saudi Arabia is in a vulnerable position: there has never been more potential for unrest and disturbance, as the handover does not make the kingdom's administration secure. Technically, King Fahd could return to power, once he has recovered, leading to fresh uncertainty. The Crown Prince's fitness to rule might yet be contested by rival relatives. At 71, he is hardly younger than the King: he may not enjoy power for long. A succession crisis may have been postponed rather than averted.
Regardless of his appointment, the 60-year-old monarchy must face two difficult issues if it is to survive. First, it must find a way of neutralising the small, but vociferous opposition. A car bomb in November outside a American-run training centre for the Saudi National Guard demonstrated how deep within the country Islamic terrorists could penetrate. That threat could increase in years to come, particularly if the Saudi regime fails to respond to a desire for a more Islamic style of government.
To forestall the growth of opposition to their rule, the Saudi royal family must continue to broaden its political base. This process was begun by King Fahd through the establishment of a consultative council, made up of appointees drawn from the great and good. The council has gained influence, but unless the regime moves further towards consensus government it, like every other absolute monarchy in history, will be doomed.
The second task is to reduce the kingdom's dependence on oil, which has left the country in financial trouble, with borrowings growing and state and corporate budgets under pressure. Diversification is easier said than done: any Saudi ruler will face opposition to change from at least some entrenched family interests. The challenge will be for the new ruler to keep his large extended family (including 6,000 princes) happy without alienating the rest of his country.