The two-phase election is the first for the seven provincial assemblies established under the constitution adopted in 2015 after initial rejection from ethnic groups in southern Nepal. The assemblies will name the seven provinces formed under the constitution and draft provincial laws.
Thursday's voting involves about 12 million people in the southern half of the Himalayan nation, nearly 80 percent of the population.
The northern, mountainous region voted on Nov. 26, and counting in some of those areas began Thursday evening.
Vote tallying in the rest of the country is expected to start Friday and take several days because some ballot boxes must be transported from remote villages to counting centers.
Chief Election Commissioner Ayodhee Prasad Yadav estimated voter turnout at 67 percent and said there were no major problems.
People holding voting cards began lining up before polling stations opened at 7 a.m. in the capital, Kathmandu.
"I am here to vote today because it is the first election for provinces, with the hope these provincial governments will be able to deliver development," said Kedar Sharan Raya, a 74-year-old retired lawyer.
"I am voting after many years because there is new hope in the country with the establishment of provinces," said Iswor Prasad Shrestha, 70, a businessman.
Security was stepped up for the election, with thousands of police and soldiers deployed. Vehicles were banned from the streets and voters walked to polling stations in their neighborhoods.
Foreign and local observers monitored the polling.
European Union observer Zeljana Zovko said they did not note any major issues in the places they visited.
Nepal's slow path to democracy began in 2006, when protesters forced the king to give up his rule. Two years later, Nepal officially abolished the centuries-old monarchy and decided a federal system would best serve all areas of one of the poorest nations in the world.
But bickering among political parties delayed until 2015 the implementation of the new constitution, which declared Nepal a republic.
Soon after the constitution took force, protests by ethnic groups in southern Nepal turned violent and left some 50 people dead.
The ethnic Madhesi group complained that they deserved more territory in the province assigned to them because they represented a bigger population. Their protests blocked the border with India for months, cutting off fuel and other supplies in Nepal.
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