The favourite is 31-year-old Luigi Di Maio, who confirmed on Monday that he was putting himself forward for the position.
Writing in a Facebook post, Di Maio said: "We're still here, stronger than ever. Now we have to finish the job; let's get to Palazzo Chigi [the Italian Prime Minister's official residence] and make Italy rise up again."
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Di Maio is currently Deputy Speaker of the Chamber of Deputies - the youngest person to ever hold the office. A law student and good speaker, always dressed in a suit and tie, he is a very different figure to the party's 69-year-old co-founder and de facto leader, former comedian Beppe Grillo.
Though the 31-year-old has long been considered the favourite to lead the Five Star Movement in the next election, in theory any party member who has held an elected position (for example on a regional council or in one of the houses of parliament) and has never belonged to another political party is eligible to stand.
Would-be candidates had until midday on Monday to apply, and voting will take place this week, with the new party leader and Five Star candidate for Prime Minister set to be announced on Saturday.
The party uses an online voting system to choose candidates for official positions - as well as to vote on draft legislation and policies - as part of its aim of 'direct democracy'.
However, the voting system, which is officially called a "consultation tool", has come under fire for a lack of transparency. A Sicilian court last week suspended the results of the Five Star Movement's regional primaries following a legal appeal by a candidate who was barred from the ballot by party leadership.
Former members have criticized the leadership's tight control over the system, as well as the fact that only a small number of supporters are signed up to the online votes: just 150,000, less than a quarter of whom actively participate in the voting, despite a total party membership of millions.
Earlier this year, Genoa candidate Marika Cassimatis was barred from the list, despite topping the poll, when Grillo judged some of her positions to be "contrary to the principles of his movement". Writing on his blog later, the party leader did not expand on exactly what these positions, or the party principles supposedly violated, were, but instead called on members to "trust me".
Cassimatis was among several politicians to criticize a rule published on Grillo's blog over the weekend, which stated that party members currently under investigation would be eligible to stand.
The rules state that such candidates are eligible to stand as long as they present a written report and documents relating to the case to party leadership.
Grillo hit back at the criticism in a separate blog post, pointing out that the regulation had been part of the party's Code of Ethics voted on by members in January. Party members found guilty of a criminal offence are ineligible to run - a rule which excludes Grillo himself, due to a conviction for manslaughter relating to a car accident in 1981.
The winner of this week's vote will not only be the Five Star Movement's candidate for prime minister, but will also become party leader. The two roles are not always held by the same person in Italian political parties, and the Movement has not previously had an official leader, something which tied into its philosophy of challenging the older 'establishment' parties.
The latest opinion polls in Italy show the Five Star Movement almost neck-and-neck with the ruling Democratic Party, both polling at around 30 percent of the vote. However, with no party set to win an outright majority, it is very unclear what the next Italian government would look like.
This is primarily because neither of the two front-runners have an obvious ally. Joining forces with one of the 'old' parties would be disastrous for the anti-establishment image of the Five Star Movement, while the Democratic Party is too far ideologically removed from the far-right Northern League to form an alliance, and would likely be forced to ally with Silvio Berlusconi's Forza Italia, a coalition which has proved troublesome in the past.
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