Crown Prince Abdullah is part of a generation of ageing royals.
Following the death of King Fahd, the Saudi Royal family moved quickly to name Crown Prince Abdullah as his successor.
Prince Sultan has also been named as the new Crown Prince.
The announcement of the succession to King Fahd was made as soon as his death was confirmed.
Saudi spokesman have stressed there will be no change in policy.
The markets have taken the news relatively calmly but behind the scenes there's still scope for plenty of turmoil, and despite the air of continuity and stability, tensions remain within the royal family.
Crown Prince Abdullah has effectively run the country since King Fahd suffered a major stroke in 1995.
But jobs will now need to be found for the members of King Fahd's court, his royal circle.
Also the new king, Abdullah, is rumoured to get on very badly with his designated successor, Prince Sultan.
In any case, they are both members of the same generation as King Fahd - all are sons of the founder of modern Saudi Arabia, King Abdul Aziz.
That means thoughts are already turning to the next generation, and who will succeed these ageing Royals.
In one hint of the jostling for position, Saudi Arabia's long term ambassador to Washington, Prince Bandar, left his job and returned home recently - perhaps to secure a position in the new administration.
Because of Saudi Arabia's pivotal place as the world's biggest oil producer, any uncertainty could have a dramatic effect on the world economy.
And in the background there's always the question of whether the Islamic militants who have been waging a sporadic campaign in Saudi Arabia will take the opportunity to revive their attacks.