MPs will come to the House of Commons later for the first time since the general election, where they will choose the next Commons Speaker.
Incumbent John Bercow is likely to return to the role, but not before facing a challenge from some MPs.
If enough call for a vote it would be the first such ballot in 175 years.
Following the formation of the coalition government, the Conservative and Liberal Democrat MPs are to sit on the same side of the Commons.
Labour’s stand-in leader Harriet Harman and her colleagues will be on the opposition benches for the first time since 1997.
Swearing in
Some 227 new MPs were elected for the on 6 May, resulting in a hung parliament and a subsequent Conservative-Lib Dem coalition.
MPs will begin being sworn in on Wednesday, assuming there is not a challenge to Mr Bercow, which would delay proceedings.
Sir Peter Tapsell, The Father of the House – meaning the MP with the longest continuous service – will preside over the appointment of the next Speaker, starting at about 1430 BST on Tuesday.
He will first ask for those supporting Mr Bercow, MP for Buckingham, to shout "Aye" and those opposing him to say "No".
Normally incumbent speakers are chosen unanimously at this stage. But if several MPs are determined to force a vote, they can do so.
There would then be a vote, with MPs passing through the lobbies.
If Mr Bercow loses this, a series of secret ballots take place until a new Speaker is chosen.
BBC deputy political editor James Landale said the process was unlikely to go this far, with Mr Bercow winning the lobby vote.
The Speaker has only been in place since last summer, when he replaced Michael Martin, who resigned over his handling of the MPs’ expenses scandal.
The last incumbent to be voted out was Charles Manners-Sutton, in 1835.
The swearing-in of MPs is expected to last into Thursday, with the most senior going first. MPs can take a religious oath or a secular affirmation of loyalty to the Crown.
The serious business of the Parliament gets under way next week, with the Queen’s Speech, outlining the coalition’s legislative agenda for the year, taking place on Tuesday.
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