"The polling was conducted peacefully and no untoward incident occurred," a spokesperson at the Election Commission of Nepal said.
Elections were held in Kathmandu-2, Kailali-6, Chitawan-4 and Bardiya-1 constituencies which were vacated by candidates winning from two constituencies representing different political parties.
Chitawan-4 was vacated by Prime Minister Sushil Koirala while Kathmandu-1 was vacated by former Prime Minister and senior leader of CPN-UML Madhav Kumar Nepal. Similarly, Bardiya-1 was vacated by Deputy Prime Minister Bam Dev Gautam and Kailali-6 was vacated by former Prime Minister and Nepali Congress leader Sher Bahadur Deuba.
The voting started at 7 am and concluded at 5 pm. The counting is likely to start tonight as soon as all the EVMs reach the district headquarters from all the polling booths, the official added.
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The results of the elections are expected by tomorrow morning, he said.
There were 251,304 eligible voters in the four constituencies, according to the Election Commission. Altogether 78 candidates were in the fray. The oldest voter was 101 year old Maheshwor Neupane, who cast his vote in Chitawan-4 constituency. In the capital city, 66.5 per cent voters exercised their franchise.