Tel Aviv - Wednesday's primaries in Israel's ruling Kadima party are crucial for the Middle East peace process.

Whoever wins has a good chance of becoming Israel's next premier.

Of the two favourites, one is a comparative hawk within the centrist party, whose election could mean more stagnation in the peace process for years to come.

The other, although a centrist too, is Israel's chief negotiator who has called the peace talks with the Palestinians a top priority.

Shaul Mofaz, second in the polls, supports a two-state solution to the conflict, but wants to postpone negotiations on the core issues of the Israeli-Palestinian imbroglio. He first wants the Palestinians to do more to fight militants. And he insists on a Palestinian state within temporary borders before a final peace deal can be reached, something the Palestinians squarely reject. Mofaz also vociferously opposes dividing Jerusalem. His positions, therefore, appear bound to lead to a stalemate.

If she wins Wednesday's vote, frontrunner Tzipi Livni for her part is likely to continue the peace negotiations the way she started them nine months ago.

Livni, like Mofaz, joined Kadima from the hardline Likud party and comes from a nationalist background. She is therefore no ultra-dove. In the delicate time in which Israel finds itself - as its ruling party is electing a new leader, and quite possibly on the eve of early elections - she has kept her position on such highly-sensitive issues as the future of Jerusalem to herself.

But she seems to understand that a peace deal without concessions on Jerusalem is impossible. "In the eyes of the Palestinians, they don't see an agreement which does not include Jerusalem," she hinted in an interview with the Ma'ariv daily published over the weekend.

According to opinion polls, Livni, 50 and Israel's foreign minister, has a two-digit lead over Mofaz, a former army chief of staff and defence minister who currently holds the transportation portfolio. But observers say Mofaz, 60, has more influence with field activists who plan to convince undecided members to vote for him. The other two candidates, former Shin Bet head Avi Dichter and Interior Minister Meir Sheetrit, trail far behind. Livni needs at least 40 per cent of the vote to win in the first round.

Israeli Prime Minister Ehud Olmert, who agreed to hold the primary because police are investigating suspicions of corruption against him, has announced he will resign immediately after the new party leader is chosen, allowing the winner to form a new coalition. Under Israeli law, he or she has 42 days to form the new government, or until early November. If he or she fails, new elections will be held by March 2009 (within 90 days), a year ahead of schedule.

Olmert could stay on at the head of a caretaker government until then and could thus in theory still meet his end-of-year deadline to reach an agreement with the Palestinians. But if Israel's attorney-general recommends an indictment against him, he is unlikely to stay on even as a caretaker premier. The Knesset, Israel's parliament, would almost certainly declare him unable to govern. Livni, his deputy, would take over.

Mofaz, according to observers, has a better chance of forming a new coalition, including a "government of national unity" with the hardline Likud. That would put off early elections - but also any breakthrough in the peace process.

Livni's associates have indicated she wants to form a coalition similar to the current one. That means she would have to court the ultra-Orthodox Shas, now Olmert's largest coalition partner after the Labour Party. But Shas declared unequivocally over the weekend that it will not sit in any government ready to negotiate Jerusalem.

That puts Livni in a difficult position, since an early poll is not in her interest. She would need time to consolidate her leadership at the head of Kadima, which would be crushed by the Likud of Benjamin Netanyahu if new elections were held, polls have consistently shown for over two years now.

For her, it would be better to go into elections as scheduled in early 2010 - with some kind of peace deal in hand.