A holiday in Tokyo limited the early reaction in equities and MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS was barely in the black.
EMini futures for the S&P 500 ESc1 rose 0.2 percent, as did Australian stocks , while Shanghai .SSEC firmed 1.2 percent as markets there returned from a long holiday, according to Reuters.
Going the other way, Thailand stocks fell 2.5 percent .SETI after the palace said in a statement that 88-year-old King Bhumibol Adulyadej's health was in an unstable condition.
Trump faces the biggest crisis of his 16-month-old campaign after a tape of him making vulgar comments about women deepened fissures with establishment Republicans.
A second debate with Democrat Hillary Clinton came and went with little immediate impact on investor thinking.
Presidential betting markets had lengthened the odds on a Trump victory, while the FiveThirtyEight site of well-regarded forecaster Nate Silver put the probability of a Clinton win at over 81 percent.
Markets generally see Clinton as a known factor with middle of the road policies. There is far more uncertainty about what a Trump administration would mean for U.S. foreign policy, trade, the economy and even governance at the Federal Reserve.
In particular, Trumps' plans to slap tariffs on imports and renegotiate the North American Free Trade Agreement (NAFTA) are seen as very negative for Mexico and Canada, which is why their currencies swing when his odds of winning change.
Both currencies gained on Monday, with the U.S. dollar down 1.4 percent on the Mexican peso at 19.06 MXN=D4 and off 0.3 percent on its Canadian counterpartCAD=D4.
The dollar dipped a touch on the yen to 102.87 JPY=, while the euro was little moved at $1.1194 EUR=.
POUND IN PERIL
Sterling was losing ground again at $1.2402 GBP=D4 after its flash crash last Friday, with dealers braced for more volatility amid concerns about a "hard" Brexit.
A survey out on Monday showed key measures of UK business investment and turnover confidence hit four-year lows in the third quarter.
"The uncertainty of leaving the single market is causing enormous concern over the future of the UK economy and the funding of its twin deficits," said analysts at ANZ.
"Moreover, the rhetoric from the UK government on immigration and EU legislation has hardened of late at the same time as the EU's position is also hardening."
China's central bank set the value of its yuan CNY=PBOC at the lowest since September 2010, and spot yuan briefly fell through the key psychological support level of 6.7 to the dollar to a six-year-low, prompting traders to wonder if it was putting the currency back on a slow depreciation path.
A similar drop in mid-July prompted a flurry of intervention by state-run banks which lasted on and off through September, but investors took the latest fall calmly, unlike sometimes in the past when such moves sparked market unease.
There was relief that U.S. payrolls data last Friday were solid enough but not so hot as to add to the risk of a rate hike from the Federal Reserve.
Fed fund futures imply less than 10 percent chance of a move in November, rising to around 65 percent for December.
In commodity markets, oil prices dipped further early Monday as players took profits following a strong rally last week spurred by talk of OPEC output cuts. [O/R]
Benchmark Brent LCOc1 was off 44 cents at $51.49 a barrel, while U.S. crude CLc1 eased 49 cents to $49.33.
Spot gold XAU= regained some ground to $1,262.76, after suffering its largest weekly drop in over three years.