TREASURIES-Long bond yields hit multiyear lows on safety buying

* Long bond yield at lowest since 2012

* Treasuries rally as stocks swoon on soft oil prices

* Yield curve for five-year to 30-year tightest since 2007 (Adds late trading, quotes, yield curve details)

By Michael Connor

NEW YORK, Jan 5 (Reuters) - U.S. Treasuries prices gained on Monday, led by a sharp rise in the 30-year bond, whose yield fell to a 2-1/2-year low on widening anxieties about global growth and Greece possibly quitting the euro zone.

The yield on the 30-year Treasury was last at 2.5922 percent, reflecting a 2-6/32 rise in price in strong volume. That yield was a low last seen in August 2012.

"Weaker equities are driving safe-haven buying in Treasuries, and then the decline in oil is raising fears about global growth," said Anthony Valeri, fixed-income strategist at LPL Financial (NasdaqGS: LPLA - news) .

Global stock markets were weaker, with the Dow Jones Industrial Average off nearly 2 percent in New York trading as oil prices touched a 5-1/2 year low and fanned fears demand was diminishing. Energy stocks were big losers on Wall Street.

Prices for benchmark 10-year Treasury notes also climbed, with gains last at 27/32 and a yield of 2.0285 percent, according to Reuters data.

Expectations for the Federal Reserve to begin raising interest rates in late 2015 have driven a selloff in short-dated Treasury securities. However, the sudden drop in oil prices has underscored fears about global demand. That, along with worries about weakness in Europe, has sparked a move into long-dated government bonds.

As a result, the spread between five-year notes and 30-year bonds narrowed to its tightest since December 2007 at 103.5 basis points. In the last seven years, on average, this spread has been around 203 basis points.

The Treasuries rally came as the euro sank to a near nine-year low against the dollar, driven lower by a European policymaker's comments that raised expectations the European Central Bank will soon open up a bond-buying program.

German regional inflation figures on Monday showed more weakness in December, adding to the downward pressure on the euro and feeding fears the euro zone will sink into disinflation. German 10-year bund yields were up.

Greek politics were also at the forefront of market thinking, according to Tom Di Galoma, head of rates and credit trading at ED&F Capital Markets in New York, as the debate around the possibility of elections later this month resulting in the country leaving the euro zone picked up again. (Editing by W Simon and Nick Zieminski)