* Bunds hit two-month highs, two-year yields turn negative
* Greece, U.S. elections underpin demand for safety
* Spanish bonds under selling pressure before Thursday's sale
LONDON, Nov 5 (Reuters) - Two-year German bond yields fell below zero on Monday as low-risk assets rallied before an uncertain U.S. presidential election and another make-or-break parliamentary vote in Greece.
Spanish bonds came under selling pressure before a debt sale of up to 4.5 billion euros on Thursday, which will include the longest dated issue to be sold at an auction since mid-2011.
Greece's government presents a new austerity package to parliament on Monday, proposals which must win lawmakers' approval if the country is to secure more aid and stave off bankruptcy. Parliament is expected to vote on the package on Wednesday.
German bonds, seen as the lowest risk in the euro zone, rallied as investors bought secure and liquid assets to protect against the risk of a surprise vote against the Greek cuts.
Two-year yields fell to -0.01 percent, the first time the debt has traded at a negative return since early September. Bund futures rose 26 ticks to 142.13.
"Against this backdrop market participants are a little bit worried about the next moves in the euro zone epic," said Marius Daheim, chief strategist at Bayerische Landesbank.
"If political decisions in Athens cause the next tranche of aid not to be paid out... then people would be looking at contagion effects once again and reassessing their current view that the crisis is contained."
A deal to keep Greece afloat is unlikely to be struck next week when euro zone finance ministers meet in Brussels, a senior EU official said on Monday.
Uncertainty over the Greek vote hit appetite for lower-rated debt across the bloc and bonds issued by Spain, seen as the next country to need a bailout, struggled. Ten-year Spanish yields rose 10 basis points on the day to 5.77 percent.
Traders said Friday's ambitious announcement of plans to launch a new five-year Spanish bond and tap 20-year paper later in the week had caught some off guard and prompted selling.
Confirmation that the European Central Bank was reviewing the terms on which it lent against Spanish securities also soured sentiment.
"We've got a chunk of supply coming on Thursday, people are setting up auction shorts (selling positions) ahead of it," one trader said.
"The five-year is going to have to come in at 5 percent to get people interested ... We are pricing out OMT (Outright Monetary Transactions) support for Spain as we meet more and more delays."
Spanish borrowing costs have been held down for months by the prospect that the European Central Bank could buy bonds if Spain asks for aid. In the secondary market, five-year Spanish bonds last yielded 4.60 percent.
In the run-up to Tuesday's U.S. election, trading activity was expected to be muted and biased towards a shift into safe havens due to the risk of a change in the direction of fiscal and monetary policy in the world's largest economy.
Markets lacked a clear consensus over whether a win for Democratic incumbent Barack Obama would be positive or negative for U.S. bonds, but euro zone debt prices were expected to track any knee-jerk shift in Treasuries whether he or Republican challenger Mitt Romney wins.
"The market is pretty dead at the moment and I would expect it to stay that way until we get the U.S. elections out of the way. On Wednesday morning, I'd expect Bunds to be doing whatever Treasuries are doing - it's as simple as that," a trader said.
Until the election, the outlook for euro zone bonds was more likely to be dominated by technical factors and the latest flashpoint in Greece's battle to get a grip on its debt, traders said.