Quite apart from doubts as to whether he is healthy enough to last a second term, Mr Yeltsin has formidable problems to resolve if his government is to progress along the road to free-market reforms and avoid further economic decline.
Although the war in Chechnya has died down with the start of negotiations, the conflict is still unresolved, and could flare up again. The economic outlook, though not entirely disastrous, has threatening clouds on the horizon.
And the fact that some 29 million people voted for Mr Zyuganov's Communist- nationalist bloc has served as a reminder of his urgent need to address Russia's dire poverty, runaway crime, the mafia, official corruption, a bedraggled army, and a host of other social issues.
Yesterday, looking considerably fitter than he has in the last week, the President made an almost cheerful television address to the nation, promising to create a new government in which there would be "a place for all of those you trust" - another hint that his new administration may include several Communists.
He also reappointed Viktor Chernomyrdin, his stalwart ally on the election trail, as his Prime Minister, instructing him to draw up a cabinet. The appointment has to be approved by the Communist-dominated State Duma (lower house of parliament), but there is little sign that it will face opposition.
With his 13-point victory in the bag, Mr Yeltsin now has to sort out the relationship between his power-hungry new head of security, retired General Alexander Lebed, and the rest of the Kremlin inner circle. Yesterday brought further evidence that the former paratrooper has already planted a hob-nailed boot on the toes of Mr Chernomyrdin, who made it clear that he was unimpressed by General Lebed's ambitions to be vice-president - a post that does not exist.
But the biggest challenges lie elsewhere. Of all the issues facing Russia - from Nato expansion to nuclear disarmament - the most important for Mr Yeltsin will be the economy. As he toured the country during his election campaign the President promised billions of dollars to the electorate in what amounted to a crude bid to buy their votes. Such was his largesse that his Economics Minister, Yevgeny Yasin, began publicly to express alarm about the risk of derailing the government's budget. Now Yeltsin is safely back in office, the government does not have the money to fulfil election pledges, despite a stable rouble and a steep drop in inflation. This year, tax collection has plunged to under 60 per cent of projected revenues, partly because of uncertainty surrounding the election and partly because the authorities agreed to go easy on some major enterprises in return for their political support.
To prevent a leap in the budget deficit, the Russian government has borrowed on the Treasury Bill market, paying interest rates of more than 200 per cent. Meanwhile, the International Monetary Fund is insisting that it meet the exacting terms of its $10.2bn three-year loan.
Although a crack-down on unpaid tax is due, no one expects the government to meet its income targets. So it is also slashing spending, and months- long wage delays seem inevitable.
A harsh autumn may well lie ahead for Russia - one that may be made even more bitter by the memory of broken election promises.Reuse content