Cardinals must be younger than 80 to take part in the conclave, so New Zealand's only cardinal, 82-year-old Thomas Williams, is too old to vote.
A two-thirds majority must be reached by the cardinals before a new pope is elected.
The 2005 conclave to elect Benedict XVI took just three ballots to reach a decision. The longest-known conclave occurred in 1830-31, requiring 50 days and 83 ballots.
Four ballots are held daily, except for the first day, when one ballot takes place in the afternoon.
If a ballot does not result in a two-thirds majority, the ballot papers are burnt and a specially-installed chimney on the chapel will emit black smoke. When a pope has been chosen, the smoke will be white.
It is expected the smoke, known as fumata, will be seen around 12pm and 7pm each day unless a decision on the new pope is reached earlier.
This pope will be the 265th. The first pontiff is believed to have been St Peter, whose pontificate ran from 33 AD to his crucifixion in 67 AD.