* U.S. economic data largely upbeat
* U.S. 2-year note auction weighs on yields (Adds analyst comments, 2-year auction results)
NEW YORK, May 27 (Reuters) - U.S. long-term bond prices rose for a second straight session on Tuesday, boosted by a combination of month-end buying by institutional investors and a relatively weak two-year auction.
There has been demand for long-term Treasuries since the middle of May for month-end purposes, analysts said, with volume moderate following a long holiday weekend in the United States.
Trading volume on Tuesday was 78 percent of the 10-day norm, which, according to CRT Capital, was unusual, given the return from a Monday holiday and partial session last Friday.
"There have been significant month-end extension trades going on, where the (bond) index actually extends," said Tom di Galoma, head of fixed income at ED&F Man in in New York. "It tells fund managers who are tied to an index to extend their duration in their portfolios."
Investors tend to extend the duration of their bond holdings when they have a good month, analysts said, driving a rally in the long end. For the month of May, both U.S. 10-year notes and 30-year bonds have outperformed.
And usually in the months of February, May, August and November, the U.S. Treasury market sees the largest duration extension trades mainly because of the new supply of 10-year notes and 30-year bonds.
Aaron Kohli, interest-rate strategist at BNP Paribas in New York, said the month-end extension trades were the largest since 2011.
In late trading, prices on 30-year Treasury bonds were last up 19/32 to yield 3.365 percent, from 3.397 percent late Friday. Benchmark 10-year U.S. Treasury notes were up 4/32 in price to yield 2.519 percent, from 2.535 percent last Friday.
A tepid two-year auction also helped the long bond rally. A weak auction suggested investors are worried about short-term rates going up and therefore they're buying the long end because they believe this sector will perform better.
The two-year note's high yield was higher at 0.392 percent from 0.390 percent at the bid deadline.
Indirect bidders, which include foreign central banks, were awarded only 18.9 percent, below the previous 23.4 percent and a 28.0 percent average. That was the weakest since January 2013.
Bond investors largely shrugged off upbeat U.S. economic data. On Tuesday, data showed orders for long-lasting U.S. manufactured goods unexpectedly rose 0.8 percent in April, compared with forecasts for a 0.5 percent decline
The numbers also showed that U.S. home prices continued to rise, beating expectations. The S&P/Case Shiller composite index of 20 metropolitan areas gained 1.2 percent in March on a seasonally adjusted basis. A Reuters poll of economists forecast 0.7 percent. (Editing by Jan Paschal)