The polls, that will elect members of the national and provincial assemblies to end almost two decades of an interim government, opened at 7 am and will conclude at 5 pm.
"The elections are taking place in a peaceful manner across the country except for some stray incidents," Election Commission spokesperson Nabaraj Dhakal told Efe news.
Two homemade bombs had exploded in Kathmandu's Manamaiju area and in Dharan, located some 400 km to the east of the capital, but did not cause any damage to life or property, he added.
By 10 a.m., around 20 per cent of the 12.2 million people who were eligible to vote had cast their votes, Sudhir Shah, one of the five election commissioners, told Efe.
"We want stability so that the country can move toward prosperity. I hope this election gives us a stable government," Yadav Dhakal, a 67-year-old retired teacher, said after casting his vote.
With a total of 25 governments in the last 27 years, three of them in the last two years, Nepal has been steeped in grave political instability for long.
In these elections, Nepalese voters will directly elect 165 national lawmakers while another 110 members of the lower house will be elected through the party-list proportional representation system, which takes into account the total number of votes secured by the parties.
Similarly, 330 members of the seven provincial assemblies will be elected directly while another 220 members will be elected through the same party-list proportional representation system.
Counting will begin after voting concludes, with results expected to be announced next week.