* Schatz yields turn negative, Bund futures at two-month high
* U.S. election influence uncertain, Greek risks on the rise
* Spanish bond yields also climb after bond auction surprise
LONDON, Nov 5 (Reuters) - Two-year German bond yields fell below zero on Monday as low-risk assets rallied before an uncertainU.S. presidential election and another make-or-break parliamentary vote in Greece.
The Greek government presents to parliament on Monday an unpopular austerity package which must gain approval in a vote on Wednesday to keep international aid payments on track and stave off the threat of bankruptcy.
German bonds, seen as the lowest risk in the euro zone, rallied. Two-year yields fell to -0.01 percent -- the first time the debt has traded with a negative yield since early September. Bund futures rose 21 ticks to 142.08.
``The situation is supportive for core markets. Not yet sufficient to trigger a massive rally but the economic situation is offering some support and also the risk element (in Greece) is favouring a bid for safe havens,'' said BNP Paribas strategist Patrick Jacq.
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, with 10-year yields rising 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 fuelled selling.
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.
``The general feeling is that if Obama gets back in we could be a bit more dovish at the Federal Reserve, but I don't see a whole lot of activity this morning and liquidity is fairly low,'' a trader said.
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 immediately after the result.
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.
The 142 level in Bund futures has provided tough resistance over the last six weeks and a break above it would have to be sustained until the market closed for technical charts to signal further price rises were on the way.