In August 1991, when Mr Yeltsin defeated the hardline Communist coup attempt, he was a leader of undisputed moral authority in Russia, the man around whom a reform programme had to be constructed. Had he disappeared from the political stage at that moment, it is doubtful that the young Westernisers who were brought into the first post-Soviet government would have been able to achieve very much. At the least, there would have been a power struggle even more intense than that which did in fact take place between the reformers and their die-hard opponents in the Russian parliament.
After Mr Yeltsin battered his enemies into submission in October 1993, by shelling the parliament building on the Moscow river, the political scene was equally fraught with uncertainty. The Russian President used his victory to create an extremely powerful executive presidency, tailored to his immediate political needs, and to establish a new parliament much weaker than its predecessor.
Had he been forced to leave politics before voters approved this remodelled system in the referendum of December 1993, it is not at all clear who would have succeeded Mr Yeltsin - for he had abolished the post of vice- president - or, indeed, whether his new constitutional order would have survived. One can well imagine the turmoil that would have engulfed Russia and the outside world if the parliamentary election victory of the extreme nationalist Vladimir Zhirinovsky that month had coincided with Mr Yeltsin being forced into retirement because of ill health.
Today, however, Russia's future is not tied so intimately to Mr Yeltsin's fortunes. Certainly, he remains the most powerful man in the country, but other politicians have grown in stature, notably Viktor Chernomyrdin, the Prime Minister. The war in Chechnya has eroded Mr Yeltsin's popularity and moral standing, and he is no longer the supreme embodiment of stability and reform that he was at the time of the Soviet Union's collapse.
Eighteen months ago, many Russians considered it essential that Mr Yeltsin should run for re-election in the presidential polls of June 1996, so that political extremists of the far-right and neo-Communist variety could be kept at bay. These fears have since receded. Mr Zhirinovsky's appeal has declined as economic conditions have improved. His party suffers from internal squabbles, and the public increasingly perceives him as a loudmouth, not a patriot.
As for Mr Yeltsin's own performance, it is common to hear the view in Moscow that history will judge him to have done his best service for his country in the late 1980s and early 1990s. His crusade against Communism, his willingness to seek power through the ballot box and his bravery in August 1991 made him a hero in his own land. Nowadays he is seen rather differently. His conversion to a more arbitrary form of rule has been particularly noticeable since the Russian armed forces started their crackdown in Chechnya last December, an operation that has caused thousands of deaths and boosted the powers of the unelected Security Council.
All this means that when progress is recorded in Russia - and it is certainly being recorded now in economic matters - people tend not to give Mr Yeltsin the credit. Inflation is being tamed, the rouble is stable, savings are growing and the financial sector and other service industries are booming, but the President's popularity ratings have hit all-time lows this year. He wields immense power, but he is probably considered less essential to the reform process than at any time since the fall of the Soviet system.
Constitutionally, it is Mr Chernomyrdin who would succeed Mr Yeltsin in the event that the President was forced out of political life. Not viewed as a heavyweight figure when he was appointed Prime Minister in December 1992, Mr Chernomyrdin has since shown considerable astuteness and strength of character in consolidating his authority.
He has proved more of an economic reformer than was anticipated when he took office, continuing the privatisation of state industries and consulting closely with the International Monetary Fund. He has distanced himself from the military's crude use of force in the Chechen conflict and is certainly no hapless prisoner of the army and security lobby.
He has also taken the important step of forming a political movement, known as Our Home: Russia, which will contest December's parliamentary elections and could serve as a vehicle for his presidential ambitions if he chooses to run next June. His aim is to consolidate moderate reformers, including bankers and industrialists, in a bloc that will strengthen the middle ground of Russian politics.
In a similar development, Ivan Rybkin, who is the speaker of the State Duma (lower house of parliament), is aiming to lead a political movement of his own into the forthcoming elections. It would position itself to the left of Mr Chernomyrdin's group, but retain an image of moderation.
The significance of these steps is that, if successful, they will inject an element of stability, even predictability, into Russian politics that has often been lacking in the four years since Mr Yeltsin became the country's first democratically elected president.
That said, it is inescapable that one of Mr Yeltsin's most important legacies to Russia will be a constitutional system that encourages the president to ignore the legislature and public opinion and offers far too much freedom of action to the military and security services. It is a system that in the wrong hands could produce tragic results, as indeed it has already done in Chechnya.
It is widely held that Mr Yeltsin imposed this constitution to punish his opponents of 1993 rather than to lay the basis for democratic government over the long term. It was a document born out of a violent political confrontation and as such it is likely to remain a focus for the continuing resentment of militant political groups. Once Mr Yeltsin leaves office a struggle to revise the constitution and restore powers to parliament is likely to flare up.
For these reasons Russia cannot yet be said to have reached the point at which it scarcely matters if Mr Yeltsin's health suddenly fails. Two attempted coups and a war in the northern Caucasus, all in the space of four years, suggest that it will take a while yet for political stability to put down deep roots.
But in many respects the outlook is increasingly promising. Some areas of the economy are thriving, the authorities have followed a consistent path of economic reform this year, the Zhirinovsky threat has waned, and in Mr Chernomyrdin Russia has a respectable leader-in-waiting. In this more mature Russia, the risks once associated with the departure or death of the head of state are not what they were.Reuse content