Spain's king is meeting Monday and Tuesday with the country's political parties following four months of political paralysis in a last-ditch effort to install a government and avoid sending voters back to the ballot box.

The national election last December was historic because it ended the country's traditional two-party system with strong showings for two upstart parties that benefited from voter outrage over soaring unemployment, corruption and austerity cuts.

But the outcome brought deadlock because no party won a majority of seats in the 350-seat chamber. The parties have tried and failed to find enough common ground to form a government.

Here's a look at Spain's unfolding political situation:

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THE PROBLEM

Acting Prime Minister Mariano Rajoy's conservative Popular Party won the Dec. 20 election with 123 seats but lost the majority that had kept it in power since 2011. Rajoy told King Felipe VI in their first post-election meeting he wasn't in a position to be a candidate for premier as he had no support from other parties.

The monarch then invited second-placed Pedro Sanchez of the leading opposition Socialist party, which won 90 seats, to try and form a government. Sanchez struck a deal with centrist newcomer Ciudadanos, which has 40 seats, but was unable to convince the far-left Podemos party, which controls 69 seats, to join him or allow him to govern by abstaining from a confidence vote. Sanchez lost the two parliamentary confidence votes last month and subsequent talks with Podemos produced more animosity than agreement.

Rajoy insists his party should head a government and wants Sanchez to support an unprecedented coalition of the country's first and second parties. The Socialists, however, reject any pact with Rajoy.

Spain has never had a coalition government.

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THE STICKING POINTS

The main hurdles to an agreement are personal or ideological.

No party wants to do business with Rajoy, chiefly because of his government's unpopular anti-crisis austerity measures and his party's links to corruption scandals. Meanwhile, Podemos doesn't want to be in a government that includes Ciudadanos — seeing it as too far to the political right. Ciudadanos feels similarly about Podemos being too radically left.

Podemos also insists on allowing the powerful northeastern Catalonia to hold a secession referendum, which all the other major mainstream parties reject.

Differences over how to deal with the nation's economic crisis — with unemployment still at 21 percent — and incessant corruption scandals are the other two divisive areas.

The Socialists and Podemos promise to roll back reforms, including a labor bill that made it easier to high and fire workers and renegotiate deficit reduction conditions. Podemos insists on raising taxes for the wealthy, removing priority status for the country's debt repayments while both parties want to raise the minimum wage. Rajoy's group claims such measures would give investors the jitters again and could wreck the country's economic recovery.

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EUROPEAN PRECEDENTS

Fragmented election outcomes and countries going weeks or months without a government aren't unusual in Europe these days.

Irish lawmakers have failed three times to select a prime minister, leaving the country in political limbo for a record near two-month period following an inconclusive Feb. 26 election that may have to be re-run soon.

Portugal also endured weeks of suspense at the end of 2015 after the winners of an October election failed to form a minority government and the losing parties joined together to create a parliamentary majority to take power.

Belgium set a European record with a massive 541 days needed to form a government following a 2010 election.

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THE KING'S ROLE

Felipe's role is akin to that of a referee. By law, following the December ballot a new government has to be in place by May 2 — otherwise the king will have to dissolve parliament and call another election for June 26.

With the deadline approaching, the king has decided to hold a third round of talks with party leaders to see if there is any last-minute chance for an agreement. He is likely to inform the parliamentary speaker Tuesday night or early Wednesday what he has decided.

"The chances of a last-minute turn of events are rather slim as parties seem to be gearing up for new elections," said Antonio Barroso, a London-based analyst with the Teneo Intelligence political risk consultancy.

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WHAT THE POLLS SAY

Polls suggest new elections wouldn't break the stalemate. No party is forecast to obtain a majority and more negotiations would be needed to form a coalition government.

A survey by pollster Metroscopia published recently by El Pais newspaper said Rajoy's Popular Party would garner 26 percent of voters against 23.1 percent for the Socialist Party, 19.5 percent for Ciudadanos and 16.8 for Podemos.

In other words, new elections in June could mean more months of political paralysis as parties again attempt to reach a deal on forming a government, a scenario not likely to please Spaniards or investors.

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Barry Hatton, in Lisbon, Portugal, Raf Casert in Brussels and Shawn Pogatchnik in Dublin, Ireland, contributed to this report.