Uhuru Kenyatta Kanu candidate |
Narc's leader, veteran opposition politician Mwai Kibaki, has 72% of the vote, with Uhuru Kenyatta of the ruling Kanu party handpicked by Mr Moi, trailing with 25%, according to the Institute for Education in Democracy a Kenyan non-governmental organisation.
Kenyan media also said that unofficial results showed two key Kanu party MPs had lost their parliamentary seats to Narc challengers, Reuters news agency reported.
In what could be a severe blow to the Kanu party, one of the MPs is thought to be current Kenyan Vice President Musalia Mudavadi, whom election officials say lost his seat in the western Sabatia constituency.
The BBC's Ishbel Matheson in Nairobi says the election has been the most peaceful poll in the country since the introduction of multi-party system in 1992.
This is despite hundreds of people finding that their names were not on the electoral register, amid opposition accusations of vote-rigging.
Fighting corruption
Three other candidates ran for the presidency, and Kenya's 10 million voters have also been electing MPs and local authorities.
Many Kenyans can only remember one president throughout their lifetimes - Mr Moi.
Mwai Kibaki voted from inside his car because of an injury |
But the vote was marred by accusations that people had deliberately been left off the electoral register and allegations that people had been paid to vote for certain parties.
ELECTION FACTS |
10 million voters
Voting for president, MPs and local authorities
Five presidential candidates
President Moi barred from standing
Polls close at 1500 GMT |
The economy is stagnating and more than half of the 30 million population live on less than $1 a day.
Kenyatta also promises a new start |
Kanu has run Kenya since it became independent from Britain. It was led first by Jomo Kenyatta - the late father of the party's presidential candidate - and then Mr Moi.
Analysts say that Mr Moi is one of the last of Africa's "big men" - who built up personality cults in the countries they ruled - often for many decades.
But the current Kanu politicians are also promising to break with the past.
Uhuru Kenyatta has had to fight claims he was only picked as a puppet for Mr Moi, who is banned from seeking re-election by the constitution.
Scores of international monitors, including 140 from the European Union, have been deployed across the country.
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