By Paul Reynolds
World Affairs correspondent, BBC News website
The new King Abdullah of Saudi Arabia led country as Crown Prince
The death of King Fahd has left Western governments reasonably confident of stability in Saudi Arabia in the short term but still worried about its longer-term future.
The short-term is assured, it is felt, because the Kingdom is in the experienced hands of Crown Prince Abdullah, now named as King, who was in charge for the past 10 years following a stroke suffered by his half-brother.
Reforms, especially in local government voting, have been instituted and the security forces seem to have got a better grip on al-Qaeda elements.
At one stage, there were real fears that the Saudi forces had been significantly infiltrated by al-Qaeda. These fears have somewhat subsided but there are still questions about how far the Saudis seek to appease al-Qaeda to avoid attacks within the country.
Saudi Arabia is a major target for al-Qaeda leader Osama Bin Laden, a Saudi himself, who hopes to overthrow the royal family. New activities by al-Qaeda in Saudi Arabia can therefore be expected in the near future as Bin Laden's supporters seek to make their mark on the new reign.
"Saudi Arabia is a real thorny problem for Washington and other Western governments, " said Rosemary Hollis, head of the Middle East Programme at the Royal Institute for International Affairs (Chatham House) in London.
"No implosion or revolution is expected, but neither the US nor the UK feel that the Saudis are there yet. They ask the Saudi government what they plan and they do not get good answers.
"Western governments are at a loss as to what role to play without making things worse. The problem for Washington is how much to get involved. President Bush has praised the Saudi reforms as part of his push for democracy in the Middle East but the local elections were then won by the conservatives. The people could be more conservative than the royal family.
"Since the attacks by al-Qaeda within Saudi Arabia, Western governments have given serious consideration to the trends in the country. They want more reforms, in the school curriculum and in the concentration on the conservative Wahabi form of Islam, for example, but if reform is the answer, how far can you go before it turns into instability?
Saudis' own 9/11
"The Saudis were as shaken by the bomb attacks on foreign compounds in May 2003 as the United States was on 11 September. Everyone, including Saudi Arabia's friends, became alarmed and there has been a constant joint effort to solve the problem."
A positive note about King Abdullah was sounded by a former British ambassador to Saudi Arabia, Sir Andrew Green. He said: "This will strengthen Saudi Arabia. Abdullah is more popular than King Fahd was. He is a wise and intelligent ruler and it is better that he is in sole charge."
Jonathan Paris of St Antony's College, Oxford, compared the succession to the old days of the Soviet Union. "This is a rerun of what happened after Brezhnev," he said. " The Soviet Union went through three leaders til they got to Gorbachev. In this case, both the new king and the crown prince are in their eighties. We should be looking eventually to the next generation.The question for King Abdullah is how far he can reform without losing control. If he goes too far, people will ask why they need the House of Saud. If he does not, the conservatives will dominate society."
Saudi Arabia is vital to US interests in the Middle East, not just because it is the source of so much oil.
With Iraq still in flames and al-Qaeda a source of influence, the Bush administration would like to see the country set on a firm course of maintaining good relations with the West on the one hand and countering unrest at home, with a mixture of reform and good security measures, on the other.
It is not an easy mixture but it is one that Crown Prince Abdullah will presumably continue to try to achieve.
Problem in common
The uncertainty surrounding the Saudi future has lent some distance to relations with Washington. The US had to move its Middle East headquarters from Saudi Arabia to Qatar for the war in Iraq, such was the sensitivity of the US military presence.
The Saudis have been more open and honest in their acknowledgement of the al-Qaeda challenge but have in turn been more open in questioning aspects of US policy in the regions, especially US support for Israel.
All this has led to some tensions but in the final analysis, their common problem in the form of Osama bin Laden is more likely to keep them closer together than their differences are liable to drive them apart.
The US needs Saudi Arabian support in Iraq. And Saudi Arabia needs the US to stop Iraq from becoming an al-Qaeda led state on its doorstep.
It is a balance of interests and one that will need very careful handling.