Zambia is voting in a presidential election caused by the death of Michael Sata in 2014.
The vote is expected to be a close contest between Edgar Lungu from the governing Patriotic Front and Hakainde Hichilema from the United Party for National Development.
The winner will serve out the remaining 18 months of Michael Sata’s term.
Zambia is due to hold a general election in 2016.
The Patriotic Front held its final rally in a suburb of Lusaka on Monday as campaigning drew to a close.
Correspondents said the Patriotic Front has been presenting a united front following some bitter infighting over its candidate.
Interim President Guy Scott, who was a close ally of the former president, told supporters that “Michael Sata is still the spirit behind this party”.
Guy Scott – a white Zambian of Scottish descent – was barred from contesting the election himself because his parents were not born in Zambia.
Edgar Lungu has portrayed himself as a candidate for continuity and has said he wants to complete economic development projects initiated by Michael Sata.
His closest rival, the economist and opposition leader Hakainde Hichilema, says he has the experience necessary to revamp Zambia’s economy.
Correspondents say the election campaign has been largely peaceful.
However, electoral commission Chairwoman Irene Mambilima said she had “noted with dismay” some violent incidents.
In a nationwide address on Monday night, Guy Scott vowed to crack down on any post-election violence.
Polling stations opened at 06:00 and will close at 18:00.
The electoral commission said that counting of the ballots should begin shortly after polls close with results due to be announced within 48 hours.
Michael Sata, who was Zambia’s fifth president, died in London last October at the age of 77.
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Zambia’s President Michael Sata has passed away at the age of 77 after receiving treatment for an undisclosed illness, the government says.
Michael Sata, who was being treated in the UK, died in London’s King Edward VII hospital on Tuesday night.
Media said that he died after “a sudden onset [of] heightened heart rate”.
It is not immediately clear who will succeed the president. The issue may be decided by the Zambian cabinet which meets on Wednesday morning.
“It is with a heavy heart that I announce the passing on of our beloved president,” cabinet secretary Roland Msiska said in a statement read out on national TV.
He said that Michael Sata’s wife and son were at his bedside.
“I urge all of you to remain calm, united and peaceful during this very difficult period,” Roland Msiska added.
Known as King Cobra for his venomous tongue, Michael Sata was elected Zambia’s president in 2011
The president’s death comes just days after Zambia celebrated the 50th anniversary of independence from the UK.
Earlier this month reports in Zambia said that President Micael Sata had gone abroad for a medical check-up amid persistent speculation that he was seriously ill.
After he left the country, Defense Minister Edgar Lungu was named as acting president.
Vice-President Guy Scott has regularly stood in for the president at official events. But he is of Scottish descent and his parents were not born in Zambia, so he may fall foul of a constitutional clause on parentage which would nullify his candidacy.
Known as “King Cobra” for his venomous tongue, Michael Sata was elected Zambia’s president in 2011.
He has rarely been seen in public since returning from the UN General Assembly in Spetember, where he failed to make a scheduled speech.
Michael Sata became president in September 2011, defeating the then incumbent Rupiah Banda whose party had been in power for 20 years.
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