* Aussie briefly falls on cliff-hanger election results

* Other major currencies steadier as Brexit continues to fade

By Ian Chua

SYDNEY, July 4 (Reuters) - The Australian dollar got off to a rocky start on Monday on heightened political uncertainty at home while diminishing global anxiety over Brexit put sterling and the other major currencies on a steadier footing.

The pound edged up to $1.3302, stabilising after an 11 percent plunge to a 31-year trough of $1.3122 a week ago in the wake of Britain's June 23 vote to leave the European Union.

While far less dramatic, Australia's general election on Saturday produced no clear winner after more than two-thirds of the votes were counted. Headlines such as 'Chaos Reigns' were splashed across front pages of some Australian tabloids.

That gave investors an easy excuse to sell the Aussie, which slid as far as $0.7410 in thin early trade, from $0.7495 late in New York on Friday. It has since rebounded to $0.7499.

"A hung parliament in Australia has not been historically conducive to good governance and policy reform, and the risk of losing the AAA/stable credit rating is not insignificant," said Annette Beacher, chief Asia-Pacific macro strategist at TDSecurities.

"While the AUD could sag on the uncertainty, fiscal policy tends to be a slow burn issue and the RBA on Tuesday is more of a marquee event for the markets."

Almost all 37 economists polled by Reuters last week expect the Reserve Bank of Australia (RBA) to keep the cash rate unchanged at a record low 1.75 percent.

Yet, there are some expectations the central bank might reinstate a clear easing bias, an outcome that should keep the Aussie under the pump.

For the other major currencies, Brexit is starting to fade as a driver with nerves soothed by promises of more stimulus from the Bank of England and talk of UK corporate tax cuts to offset the shock of leaving the EU.

The clear fallout from Brexit is that investors no longer expect the Federal Reserve to hike U.S. interest rates this year, while other major central banks are seen poised to ease policy further.

Highlighting the theme of lower rates for longer, U.S. Treasury yields plunged on Friday with the benchmark 10-year briefly reaching a four-year trough of 1.382 percent, before closing at 1.461 percent.

The euro stood at $1.1130, versus $1.1139 on Friday, and it was little changed at 114.31 yen. The dollar was steady at 102.62 yen.

But some traders say the impact of Brexit could take longer to emerge given nothing concrete has been set after the referendum, including when and how that will happen.