More than 15 million eligible voters are choosing a 275-member parliament and provincial assemblies.
Voting is brisk with long queues of voters in mountainous districts.
The centrist Nepali Congress Party is taking on an alliance of Maoist former rebels and the opposition Communist UML party.
The country is voting in two phases, with the second phase to be held on 7 December.
Voting was paused in three polling centres after an explosive device was found at one and acid was sprinkled on ballot boxes at two others, local officials said according to AFP news agency. There were no reports of injuries.
The polls are the first under a new constitution that paved the way for sweeping changes to the political system.
It was adopted after years of negotiations following a 10-year civil war between the security forces and Maoist insurgents.
Under the new constitution, a proportion of seats in the federal and provincial assemblies will be allocated to women, people from indigenous communities and the lowest Dalit caste.
Amid an extended period of political instability since the end of the war, Nepal has run through an array of different leaders and corruption has burgeoned. That has impeded efforts to rebuild following the devastating earthquake in 2015.
“The government changes every nine months and don’t get to do any work. Instead they fight for power. We hope that will change,” farmer Gyan Bahadur Thapa told AFP after casting his ballot in Chautara.
“We need roads, water supply, electricity, health care and jobs so our children are not forced to go abroad to work,” housewife Rita Shrestha told Reuters news agency.
In some districts, voters walked for hours to reach the polling stations where they then waited in chilly but sunny weather to cast their votes.
The BBC World Service’s South Asia editor, Anbarasan Ethirajan, says the Nepali Congress Party faces a tough battle against the left alliance.
He adds that there are hopes that the new government will bring unity to the country and give a new impetus to the reconstruction programme. (Courtesy BBC)