* Treasury sells $29 billion of seven-year debt * High yield in auction comes in below market expectations * Weakness in inflation-linked debt seen problematic for Fed * Fed buys $1.53 billion of bonds due 2036-2043 By Luciana Lopez and Karen Brettell NEW YORK, May 30 (Reuters) - U.S. Treasuries traded nearly unchanged on Thursday as investors waited for clues about the strength of the economy and future moves by the U.S. Federal Reserve, which has hinted recently it could soon slow its massive monetary easing program. Prices briefly edged higher after a sale of $29 billion in 7-year debt fetched a lower yield than markets had expected, with solid demand for a second auction in a row this week. A five-year note auction on Wednesday was met with strong demand, although a two-year note auction on Tuesday did not fare as well. But the price gains proved ephemeral, as investors were reluctant to change positions as uncertainties remain about the Fed's future course of action. "Investors are in a wait and see mode, just like the Fed," said Millan Mulraine, director of U.S. research and strategy at TD Securities in New York. "If you're an investor with a position in Treasuries right now, you essentially want to sit on your hands in the next few days," he added. The strength of the world's biggest economy is the key question for Treasuries investors now: Is it strong enough for the Fed to slow or even stop buying $85 billion per month in Treasuries and mortgage-backed securities? Or is the central bank's support still crucial in the face of fiscal headwinds? Markets have been especially sensitive to these questions after Fed Chairman Ben Bernanke said last week the bank may decide to taper its program of buying Treasuries and mortgage-backed securities within the next few Fed policy meetings if data shows the economy is gaining steam. The resultant dramatic surge in Treasuries yields this month is leaving many investors struggling to figure out whether the rise will continue or if the market is oversold. Data next week showing how many jobs employers added in May is seen as the catalyst for deciding the next large rate move. "We've reached an uneasy equilibrium in the market, where we can easily see the prospect of much lower or much higher rates," said Aaron Kohli, an interest rate strategist at BNP Paribas in New York. Benchmark 10-year notes were last up 2/32 in price to yield 2.114 percent, compared to 2.119 percent late on Wednesday. The yields have jumped from 1.61 percent at the beginning of May to reach a 13-month high of 2.24 percent in overnight trading on Wednesday. A dramatic selloff in the inflation-linked bond market, however, may complicate the Fed's objective of encouraging borrowing in order to fund economic expansion. The so-called real yield, which is the amount a bond yields after accounting for inflation, has been trading at negative levels for the past few years, which has made it attractive for companies and other borrowers to issue debt at very cheap levels. "This is the Fed's lever for making the economy go," said Kohli. After the recent selloff, however, "the market seems to be placing no possibility at all on the prospect of inflation." Treasury Inflation-Protected Securities (TIPS) staged a dramatic selloff on Wednesday even as Treasuries prices rose. Ten-year real yields are now trading at around negative 15 basis points, meaning a borrower would earn 15 basis points per year from issuing debt, in from around negative 72 basis points at the beginning of May. The release of April's Personal Consumption Expenditures index on Friday, the Fed's favored inflation gauge, will be closely watched for a further drop in price inflation. The index has fallen to a 3-1/2-year low of 1.0 percent. The Fed bought $1.53 billion in debt due 2036 and 2043 on Thursday as part of its bond purchase program.