Pakistanis are voting for more than 40 seats of the federal and provincial legislatures amid tight security.
Khurshid Khan, an official at the Election Commission of Pakistan, said more than five million people are expected to vote in the August 22 poll for 15 seats in the national parliament and 26 in provincial assemblies.
The by-election in one constituency in the northwestern province of Khyber Pakhtunkhwa was postponed because of Taliban threats.
Polls are being held in constituencies vacated by candidates who won more than one seat in the general elections in May.
In addition, at least three constituencies are vacant because lawmakers were killed by Islamist militants.
Pakistani law allows candidates to contest elections for multiple constituencies but permits them to retain only one.
All the major political parties are participating in the by-elections, but the results are not expected to result in any major change to their standings in parliament.
Based on reporting by dpa and RFE/RL's Radio Mashaal