By Gavin Jones

ROME (Reuters) - The unruly comedian who founded Italy's anti-establishment 5-Star Movement is no longer whipping crowds into a frenzy at political rallies, but 5-Star, against all predictions, has proved it can outlive its creator.

Beppe Grillo's fiery rhetoric, which almost got the movement into power in a 2013 national election, frightened off many moderate voters and his retreat to the theatrical stage the following year marked 5-Star's coming of age, not its demise.

It paved the way for a more serious makeover that has appealed to the center of Italian politics, positioning the party a close second to Prime Minister Matteo Renzi's Democratic Party and favorite to win the mayor's job in Rome on Sunday.

Scepticism was widespread when Grillo, now 67, announced he was stepping back in a blog portraying himself as Forrest Gump, the slow-witted, athletic character played by Tom Hanks in the eponymous 1994 movie.

Grillo and the movement he founded in 2009 were seen as virtually the same thing. His supporters, elected to parliament with no political experience, were known simply as "Grillini," meaning "little Grillos".

"I'm pretty tired, as Forrest Gump would say," he wrote in November 2014 beneath a mock-up of himself as Gump telling an enthusiastic group of followers he will stop running to and fro across the United States.

Most commentators assumed it was another of his jokes, but Barbara Lezzi, an influential 5-Star senator, said the blog post did not take its parliamentarians by surprise.

"Beppe had come to see us several times in the Senate and let us know what he had in mind," she said. "He always wanted the movement to be able to stand on its own feet."

Grillo set up a more formal leadership structure, with a five-member committee, or "directorate," approved by an online poll, taking over day-to-day running of the movement.

"5-Star is evolving from a 'movement', made up of followers of a charismatic leader into a 'party' with an organization and an internal structure," said Raffaele De Mucci, a political science professor at Rome's LUISS university.

"Rome will be a fundamental test if its mayor is elected, because it offers the chance to disprove the theory that it is too inexperienced to govern."

SETBACKS

Its candidate Virginia Raggi, a softly-spoken, 37-year-old lawyer, is about as far from Grillo, personality-wise, as is possible and while she adheres to his anti-establishment message, her campaign is focused on everyday city issues such as transport and rubbish collection.

Many of the party's ideas appeal to left and right-wing voters alike, something that sets 5-Star apart from other European anti-system parties such as the leftist Syriza in Greece and Podemos in Spain, or the far-right National Front in France.

But its progress has been anything but smooth since its 2013 breakthrough. It has had setbacks at European and local elections and been so beset by internal divisions that 37 of its original 163 parliamentarians have left to join other parties.

It is widely criticized for an alleged lack of internal democracy and, in the handful of towns and cities it controls, several of its inexperienced mayors have run into trouble.

So why has its appeal continued to grow?

Weak economic and jobs growth, and a stream of corruption scandals affecting the established parties have certainly helped. Its trademark call for "honesty" in public life continues to resonate, and remains its chief asset.

But analysts say it has outgrown its image as purely a party of protest and its proposals are now also being taken seriously.

These include universal income support for the poor, tougher penalties on white collar crime and tax evasion, building more prisons, closing down or privatising many publicly owned companies and cutting taxes for small businesses.

It wants to cut state generous pensions that are not fully funded by contributions and says the Bank of Italy should be owned by the state instead of the private banks it supervises.

Most controversially, it proposes a referendum on whether Italy should remain in the euro zone, though it has sharply cut its anti-euro rhetoric since Grillo's role declined and now seldom addresses the issue. "We have other priorities at the moment," said senator Lezzi.

The party's support comes mainly from the young and well-educated, data shows, while it has little following among pensioners. It gets a generally hostile press in Italian media.

"They dismiss us as populist as a way to avoid discussing our proposals," said Luigi Di Maio, the 29-year-old deputy speaker of the Chamber of Deputies who is tipped to be 5-Star's candidate for prime minister at the next election, due in 2018.

"We are not populist. Our policies, from welfare to spending cuts and justice reform, are detailed and fully funded."

Grillo maintains a behind-the-scenes role as "guarantor" of the party's internal rules. Its new, less aggressive leaders like Di Maio, offer voters a more reassuring public face.

Francesco Galietti, of Rome-based consultancy Policy Sonar, said 5-Star will have trouble maintaining its anti-establishment image if it assumes more positions of power.

"Italy's establishment has a long history of making peace with odd political bedfellows and if it tires of Renzi it may well seek to favor the normalization of the 5-Star Movement," he said.

(Editing by Philippa Fletcher)