UPDATE 2-Long German yields hit 2-month lows after well-bid auction

* Investors rethinking long-term policy path

* Germany's bond yield curve flattest this year

* U.S. curve flattest in a decade

* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Updates prices)

LONDON, June 21 (Reuters) - German 30-year bond yields hit two-month lows on Wednesday, narrowing the gap with shorter equivalents to its lowest this year, after investors bid twice the amount of 30-year debt offered at an auction.

Demand for this debt has ratcheted up in recent weeks as investors have re-evaluated the pace of global monetary tightening against the backdrop of stubbornly low inflation and falling oil prices.

That was in evidence even before Germany's auction with yields, which normally rise ahead of new sales as investors make room in portfolios for the new supply, grinding lower.

After the debt office announced it would sell just 800 million euros of the bonds despite the high demand, yields fell further to touch their lowest level since mid-April.

The gap between long- and short-dated bond yields was the lowest it has been this year, a trend called curve flattening which develops when investors start to question the long-term path for monetary policy and interest rates.

"As yields are turning downward there is more juice at the longer end and this is drawing interest," DZ Bank strategist Daniel Lenz said.

"It is a continuation of this bullish flattening mode we have seen in recent days as we see crude prices dropping with low inflation expectations."

A slump in oil prices to multi-month lows has reinforced the weak outlook for inflation that the euro zone central bank cited for its cautious approach at a meeting earlier this month.

Weak consumer price growth has also made investors question whether the U.S. Federal Reserve will be able to raise interest rates again this year after a hike last week.

A U.S. policymaker said on Tuesday that low yields meant the central bank would have to be careful about raising rates further.

The Bank of Japan said it will lag well behind the Fed in dialling back its massive stimulus programme, with inflation far from its 2 percent target.

German 30-year bond yields were down 2 basis points at 1.05 percent on Wednesday, having hit a two-month low of 1.035 percent earlier in the session. Ten-year equivalents were flat at 0.27 percent.

Two-year yields were up 1.6 bps fraction lower at minus 0.652 percent, which meant the gap to thirty-year equivalents shrank to its lowest level since late December at around 168 bps.

The same trend has been particularly noticeable in the United States where its curve is the flattest it has been in a decade .

For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.bi z / c m s / ? p a g e I d = l i v e m a r k e t s

(Reporting by John Geddie; Editing by John Stonestreet and Raissa Kasolowsky)