According to inquiries by Russian newspapers, prosecutors and courts, Mr Yeltsin's supporters in regional administrations and electoral commissions may have exaggerated voter turnouts so that they exceeded the required 50 per cent of the electorate needed to validate the referendum.
The accusations have grave implications for Russia's stability, because the constitution affords Mr Yeltsin sweeping executive powers and is the basis of the political system that he has built since crushing an armed revolt in Moscow last October. The allegations will reinforce the determination of his enemies to remove him on the grounds that his powers are illegitimate.
The threat of political turmoil is leading some Yeltsin advisers to advocate the postponement of presidential elections scheduled for 1996. That might prompt anti-Yeltsin elements to make another attempt to remove him.
The details of the alleged electoral fraud have appeared in both opposition and pro-reform media. Legal authorities have sometimes confirmed them. The supervisor of a Moscow polling station committed suicide after the referendum and left a letter confessing that he had 'grossly deceived the people', according to one newspaper, Novaya Yezhednevnaya Gazeta.
In the Far Eastern province of Amur, prosecutors said local officials had falsified 16 out of 22 lists of votes from one polling station. It appears that Amur voters did not, as officially reported, approve the constitution.
The irregularities occurred partly because heads of local administrations, most of them Yeltsin appointees, organised the electoral commissions that gathered and checked votes.
According to final results, 54.8 per cent of eligible voters took part and 58.4 per cent supported the constitution. The Central Electoral Commission published these figures almost two weeks after the referendum, but waited until mid-February before specifying the exact number of eligible voters.
Eventually, that number was put at 106.2 million. However, eligible voters were estimated at 107 million or more in a referendum in April 1993 and in the December campaign. The lower final figure reduced the turnout required to ratify the vote.
Official results indicate that 58.2 million people voted in the referendum. Before the referendum, electoral commissions at city and district level were abolished. The Central Electoral Commission was supposed to check 95,000 lists of votes; 19,000 lists were flawed, but none was invalidated before the outcome was declared.