By Thomas Escritt

BERLIN (Reuters) - Germany's election winner Friedrich Merz wants to form a government quickly in order to revive a moribund economy, hike defence spending and tackle diplomatic challenges ranging from a confrontational Trump administration to ending the Ukraine war.

But Merz's conservatives need at least one coalition partner to govern and face potentially months of difficult negotiations before a stable government is likely to emerge.

Here is what happens next.

WHAT MAJORITIES ARE AVAILABLE IN PARLIAMENT?

Together, Merz's conservative CDU/CSU bloc, with 208 seats, and the Social Democrats (SPD) of outgoing Chancellor Olaf Scholz, with 120, have 328 seats, giving them a slim majority in the 630-seat parliament. Mathematically, the second-placed Alternative for Germany (AfD), with 152 seats, could also ensure a stable majority for Merz but the conservatives and all other parties refuse to work with the far-right party.

Political analysts expect a so-called 'grand coalition' comprising the conservative bloc and the SPD to form Germany's next government.

HOW IS A GOVERNMENT FORMED?

Once the two parties have agreed to talk, they each delegate working groups to meet and thrash out a common agenda for each policy area. Together, the two parties draw up a government programme - essentially a contract for the policies and laws they plan to enact over their four years in government together.

The programme then has to be approved by the leadership of the parties involved. They have also been trying to decide which party gets which ministry and who gets to run it. Powerful ministries like finance and the economy, and prestigious ones like foreign, are often the focus of fierce haggling.

This is also a moment for horsetrading within the parties: each faction in the two big-tent parties (the conservative bloc and the SPD) will stake a claim to a role in government.

The SPD's membership will have to vote to approve any recommendation by the leadership to enter a coalition. Few of them are naturally keen on governing with a centre-right party, least of all one led by Merz, a combative right-wing conservative with a very different style and ideas to those of his more emollient, centrist predecessor, Angela Merkel.

That gives the SPD negotiating team an advantage: give us more policies, or ministers, they can say, and we have a better chance of getting our restive membership on board.

If they go too far, however, negotiations could collapse, leaving Merz with the unattractive choice between forming a weak minority government, calling fresh elections, or going back on his earlier promise not to work with the AfD. Doing that would likely split his party.

In any event, Scholz remains as acting chancellor until Merz is sworn in.

WHERE ARE THE PARTIES AT ODDS?

Merz has promised stricter border controls, even permanent checks on the borders, and direct expulsion of migrants at the borders, all things the SPD opposes, saying they violate human rights and European law. He also wants to undo one of the SPD's signature achievements: a new, simplified citizenship law designed to allow foreigners to integrate more easily.

On economic and social policy, Merz wants to scrap an unemployment benefit introduced by the previous SPD-led government, though here the SPD recognises a need for reform.

The conservatives want corporation tax cuts, while the SPD wants high earners - including companies - to pay more. The SPD wants to increase the minimum wage to 15 euros an hour from its current level of 12.58 euros. 

WHERE DO THEY AGREE?

Both want to spend more on infrastructure, and all parties agree something must be done about the totemic spending cap - a constitutional rule limiting borrowing each year that was introduced in times of plenty but which is interfering with urgently-needed infrastructure spending. While the parties have different views on how it should be reformed, most observers believe there is room for agreement.

Here, though, they run up against the need for a two-thirds parliamentary majority to reform the constitution. That can only be reached with the votes of the Greens and the Left party. Both will want support for signature projects in return.

In particular, the Left, sceptical of defence spending, will want to see some concessions on social policy - perhaps on housing - if they are to support a reform that lets the government spend more on supporting Ukraine.

(Reporting by Thomas Escritt and Rene Wagner; Editing by Gareth Jones)