By Vidya Ranganathan and Dhara Ranasinghe

SINGAPORE/LONDON (Reuters) -From ho-hum debt auctions to plunging long-term bond prices, investors are sending a clear message to governments that in the current climate of uncertainty they need to pay more to borrow for decades ahead.

Yields of government bonds with the longest maturities have risen sharply not just in the United States, where the chaotic first months of Donald Trump's second term in the White House are causing investors to demand better returns on their bond holdings, but also in Japan and Britain.

Multi-billion dollar government bond sales, which used to be a seamless process for big economies, are becoming the arena for bond vigilantes questioning government profligacy and inflation outlooks. In Japan and the United States, bond markets do not seem to like the tax cuts the ruling parties are seeking.

This week's poor 20-year U.S. bond sale and Japan's worst auction result since 2012 served as a wake-up-call for the market, coming right after Moody's became the last of three major rating agencies to strip the United States of its top triple-A credit rating because of its growing debt.

"Investors are thinking that if we are in a world where debt continues to deteriorate, and the growth dynamic is more fragile, the risk premia we demand to hold these bonds should rise, and that's what's happening now," said Zurich Insurance Group chief markets strategist Guy Miller.

In the coming weeks, Japan, Germany, the U.S. and the UK will be offering 10-year and 30-year bonds.

"Investors are challenging issuance here," said Miller.

In theory, governments could spend less or tax more to reassure investors, but belt-tightening is hardly an option given concerns about the impact of Trump's trade war on the global economy.

TERM PREMIUM

Most of the selling of Treasuries, UK gilts and Japanese government bonds (JGBs) has been at the long end of the curve, driven by concerns that Trump's trade war and tax cuts will stoke inflation and force governments to spend more.

UK 30-year gilt yields have hit their highest since the late 1990s this year. U.S. 30-year yields are at 5.09%, up 70 basis points since March.

U.S. public debt is around 100% of gross domestic product and projected to rise to 134% over the next decade, according to Moody's.

The root reason for the selling is what investors call the "term premium", or the extra yield bondholders expect for locking in their money for a long time.

The term premium on 10-year U.S. Treasuries, the extra returns investors demand for holding longer-term bonds rather than rolling over short-term debt, is estimated at 0.79%. That seems too low in this environment - below levels in 2011, when U.S. debt was at similar levels, and a fraction of the 5% during the stagflation of the 1970s.