Boris Yeltsin was Russia's first democratically elected President, chosen in 1991 for five years under the Soviet-era constitution. Tension has surrounded his campaign for a further term, which will be four years under the constitution of 1993. Rivals have suggested there could be vote-rigging.
In addition to 1,200 international observers, monitors from political parties are going to the 95,000 polling stations across the country's 11 time zones to check the official count. Some107 million people are eligible to vote.
Apart from Mr Yeltsin, nine other politicians are running. A preliminary result should be available today. If no candidate wins an overall majority, the top two go forward to a second round in which the first past the post wins. The second round must be held within 15 days of the announcement of the first-round result. A run-off is likely to be held on 7 or 14 July.