The Independent Electoral Commission of Nigeria says over 31,000 police had been deployed, as well as 87 gunboats, to prevent, or deal with, any electoral violence.
Nigerians voted on Saturday to elect new governors in two states with security forces out in numbers to prevent any violence following pre-vote attacks.
The two states, southern oil-rich Bayelsa and central Kogi, are among seven states where gubernatorial elections are held at different times from the general election due to court rulings.
Bayelsa has been ruled by the main opposition People's Democratic Party since Nigeria returned to civilian rule in 1999.
Voting opened late in most polling stations in the state, with long queues of voters forming in Yenagoa, the state capital, and elsewhere.
In Otuoke, the hometown of former president Goodluck Jonathan, party thugs fought over distribution and late arrival of voting materials.
The polls were officially to close at 1300GMT, but electoral officials said everybody queuing would be allowed to vote even after the deadline.
Some 900,000 voters are eligible to vote for the candidates of 45 political parties in 1,804 polling units across the state.
The leading candidates are David Lyon of President Muhammadu Buhari's All Progressive Congress (APC) and PDP's Douye Diri, a former senator.
The winner of the election will replace PDP Governor Seriake Dickson, who is stepping down after two four-year terms, the legal maximum.
The Independent Electoral Commission of Nigeria said over 31,000 police had been deployed, as well as 87 gunboats, to prevent, or deal with, any electoral violence.
Police helicopters were hovering over Yenagoa, while soldiers and anti-riots police mounted roadblocks at major points.
This week, a staffer at a radio station was shot dead and many injured during an attack on a political rally in Bayelsa, and in Kogi state a campaign office was burnt down.
"Already there have been several instances of violence at election campaign rallies in both Bayelsa and Kogi states," Amnesty International said on Friday.
"Amnesty International has received reports of supporters of some politicians violently targeting political opponents, real or perceived," it said.
Voters said they hoped for a peaceful election day.
"We crave a free, fair and hitch-free elections in Bayelsa. Everybody should be allowed to exercise his or her franchise without harassment and intimidation," said Joseph Cookey, a textile trader in the southern city of Port Harcourt.
Housewife Alice Ebere urged "politicians to shun violence and allow the wish of people to prevail".
In Kogi where incumbent Governor Yahaya Bello of APC is seeking re-election against Musa Wada of PDP, a boy was shot in the leg when a group of people stormed into a polling unit and snatched the ballot boxes.
Local reports also said some party agents were beaten up at another polling booth in the state.
History of electoral violence
Nigeria, Africa's most populous nation, with 190 million people, has a long history of electoral violence, vote-buying, ballot-stuffing and voter intimidation.
Dozens of people were killed during the 2019 general election which returned Buhari to power.
In 2011, hundreds of people were killed in post-election violence, mostly in northern Nigeria.
Buhari, the 76-year-old general who headed a military regime in the 1980s, has promised to reform the country's electoral system to ensure free, fair and credible elections.