PRAGUE, Oct 11 (Reuters) - The Czech Republic finds itself after Saturday"s election in the unusual position of having a combined opposition majority and a billionaire prime minister who has yet to give up attempts at forming a new cabinet. And President Milos Zeman is in intensive care due to complications caused by an undisclosed chronic illness, unable to oversee talks to form a new government. read more Here"s what could happen next. FIRST STEPS By convention, the president should talk to all parties and ask one of them to negotiate with partners and propose a government. But with Zeman in hospital, the parties plan to talk among themselves. The first parliamentary session will be held within a month of the election and must elect the new parliamentary speaker, a crucial test of control in the chamber. After that, the outgoing government resigns and the president appoints a new prime minister and cabinet, but there is no deadline for this process. ZEMAN APPOINTS BABIS Zeman could give his ally, Prime Minister Andrej Babis, the first chance to form a government on the basis that Babis"s centrist ANO party won the biggest single share of seats. Zeman had in the past said the biggest party would have the first chance. If Babis is appointed prime minister and loses a confidence vote, mandatory within 30 days of appointment of the cabinet, he must resign, but his cabinet would remain in office until the president appoints his second choice. The process could take months. If the president"s second choice also fails, the lower house speaker can pick the prime minister. This is expected to be a representative of the opposition parties that now hold a majority. His or her choice of prime minister would ensure the transfer of executive power. ZEMAN APPOINTS OPPOSITION LEADER Opposition groups, the centre-right Together and the liberal Pirates/Mayors, have 108 seats in the 200-seat lower house and have declared they will form a government. They have said they will refuse any approaches from Babis to join forces. If Babis gives up the ambition to build a new cabinet, or if Zeman accepts the parliamentary numbers, the president can appoint the opposition candidate, Together leader Petr Fiala, as prime minister as his first choice. INCAPACITATED PRESIDENT If the presidential seat is vacated, the right to accept a government"s resignation and appoint a new prime minister and cabinet goes directly to the lower house speaker, elected at the first parliamentary session. If the president is incapacitated, the two houses of parliament - both now opposition-controlled - can make a declaration saying as much. That would also transfer his government-appointing powers to the speaker. The president can challenge a declaration on him being unable to perform his duties at the Constitutional Court.