ROME (Reuters) - More than a week after inconclusive national elections, Italians are no nearer knowing the make-up of their next government, and are likely to have to wait many more weeks until they find out.

The March 4 election ended in a hung parliament, with a rightist coalition winning a combined 37 percent of the vote and the anti-establishment 5-Star Movement emerging as by far the largest single party in parliament on 32 percent.

This meant both groups fell well short of a working majority in the two chambers of parliament and left the defeated centre-left Democratic Party (PD) as a potential kingmaker.

However, the PD has said it wants to go into opposition, and there is no sign of any warming between the 5-Star and the largest party in the conservative bloc, the far-right League -- seen by many as the two clear victors of the election.

So what happens now?

PARLIAMENT OPENS

The next important milestone will be March 23, when the new parliament sits for the first time and immediately starts electing speakers for both the upper and lower houses, thereby giving an indication of which parties are working together.

If there are no deals, the vote for the lower house speaker could drag on for days, because the victor there must secure an absolute majority. By contrast, the Senate vote goes to a run-off ballot after just three rounds of inconclusive results.

The 5-Star and League have said they expect to get the speakership of one house each. Media reports say former prime minister Silvio Berlusconi has threatened to break his alliance with the League if it strikes a deal on this with 5-Star. But if the two parties do vote together to secure these prestigious posts for themselves, that does not automatically mean they are ready to take it to the next stage and form a government.

As soon as the two speakers are picked, parliamentary party groups can form, opening the way for presidential consultations.

THE PRESIDENT

President Sergio Mattarella will play a key role in trying to sort out the political deadlock. If the speakers are elected quickly, he will start his consultations with party leaders immediately after Easter, which falls on April 1. He will see each group individually and listen to their views on how to end the stalemate. A state official, who declined to be named, said the president’s office had no deadline for finding an accord and was ready to undertake two or even three rounds of consultations before hopefully breaking the deadlock. After the 2013 election, which resulted in a hung parliament in just the Senate, it took 40 days from the opening of parliament to find a coalition.

POLITICAL SOLUTION

The president will initially seek a “political solution”, with three possible outcomes in view -- an alliance between the PD and the right, the PD and 5-Star or 5-Star and the League.

If none of these three scenarios play out, some analysts say Italy could head towards a minority government, where one party or group takes office and is kept alive in parliament thanks to the external support of another bloc or party. Italy has only ever had two such administrations, in 1963 and 1976, but they lasted only a few weeks each. Mattarella would almost certainly seek firm guarantees that such a government could survive at least one year this time around.

“GOVERNMENT FOR ALL”

If no political solution is found, Mattarella would then look to see if he could find support for a “government for everyone” or “president’s government”, hoping that all the parties might support an administration probably made up of technocrats with a limited agenda -- such as drawing up a 2019 budget -- to prepare the way for new elections next year. Both the 5-Star and the League have ruled out supporting such a move.

EARLY ELECTIONS?

The state official said Mattarella would take his time and ruled out any possibility of a return to the polls before the summer months of July and August. So, in the event of deadlock, the earliest date for a new vote would be October. Fresh elections have not been held immediately after inconclusive votes at any point in modern Italian history. Since 1946, the shortest legislature lasted 20 months, between 2006-2008.

WHO GOVERNS ITALY IN THE MEANTIME?

Outgoing centre-left Prime Minister Paolo Gentiloni must formally resign before the new parliament meets. He will remain in a caretaker capacity, carrying out day-to-day duties.