More than 12.2 million voters are eligible to exercise their voting rights in the second phase of the polls.
The voting is taking place for 128 constituencies of Parliament's House of Representatives and 256 seats of Provincial Assemblies in 45 districts.
In total 4,482 candidates, including Prime Minister Sher Bahadur Deuba, will be trying their fate in the final phase.
For the House of Representatives, 1,663 candidates are contesting and 2,819 candidates are trying for the Provincial Assemblies.
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Vote counting is expected to start later today.
The first phase of the polls in the land-locked country was successfully held in 32 districts on November 26.
Around 200,000 security personnel, including the Army, have been deployed for the polls in an attempt to step up security in the wake of explosions at various parts of the country ahead of the elections.
This is for the first time that elections for Parliament and Provincial Assemblies are being conducted under the new Constitution promulgated in September 2015.
The House of Representatives consists of 275 members. Of them, 165 are elected directly under the First-Past-the-Post system while the remaining 110 come through Proportional Representation system.
The elections are being seen as the final step in Nepal's transition to a federal democracy following a decade-long civil war till 2006 that claimed more than 16,000 lives.
While many hope Nepal's first state elections will hasten regional development, others fear they will spark a fresh wave of violence.
In 2015, when Nepal adopted a new Constitution that split it into seven states, dozens of people were killed in ethnic clashes over territory and rights.
The polls are a major step toward implementing the new Constitution.