Japan's Nikkei 225 was down 0.1% at 39,458.86, while the Kospi in Seoul rebounded to pick up 0.5%, to 2,576.30.
Australia's S&P/ASX 200 edged 0.1% higher to 8,204.80.
Chinese shares also climbed. Hong Kong's Hang Seng gained 0.9% to 20,729.01. The Shanghai Composite index also was 0.9% higher, at 3,413.47.
Trump has promised to slap blanket 60% tariffs on all Chinese imports, raising them still more if Beijing makes a move to invade the self-governing island of Taiwan.
Investors are adding to bets built earlier on what the higher tariffs, lower tax rates and lighter regulation that Trump favors will mean. Higher tariffs on imports from China would add to the burdens Beijing is facing as it struggles to revive slowing growth in the world's second-largest economy.
Higher tariffs on imports from China, Mexico and other countries also would raise the risk of trade wars and other disruptions to the global economy.
But Trump's win raised expectations that Beijing may ramp up its spending and other stimulus to counter such trends. The Standing Committee of China's legislature is meeting this week and is expected to announce further measures by Friday.
On Wednesday, the U.S. stock market, Elon Musk's Tesla, banks and bitcoin all stormed higher, as investors made bets on what Donald Trump's return to the White House will mean for the economy and the world. Among the losers the market sees: the renewable-energy industry and potentially anyone worried about higher inflation.
The S&P 500 rallied 2.5% to 5,929.04 for its best day in nearly two years. The Dow Jones Industrial Average surged 3.6% to 43,729.93, while the Nasdaq composite jumped 3% to 18,983.47. All three indexes topped records they had set in recent weeks.
The impact of Trump's second term will likely depend on whether his fellow Republicans win control of Congress, and that's not yet clear.
Investors see Trump’s policies potentially leading to stronger economic growth. That helps push prices down and yields up for Treasurys. Tax cuts under Trump could further swell the U.S. government’s deficit, increasing borrowing and forcing yields even higher. The yield on the 10-year Treasury jumped to 4.43% from 4.29% late Tuesday, which is a major move for the bond market. It’s up substantially from August, when it was below 4%.
Investors expect the incoming president's policies, particularly higher tariffs, to fan inflation and add costs to U.S. household bills. Sharp cutbacks in immigration could also leave businesses shorthanded, forcing companies to raise wages for workers faster and put more upward pressure on prices.
Much of Wall Street's run to records this year was built on expectations for coming cuts to interest rates by the Federal Reserve, as inflation has headed back down to its 2% target. Easier interest rates help boost the economy, but they can also give inflation more fuel.
The Fed will announce its latest decision on interest rates Thursday, where the expectation is still for a cut, according to data from CME Group. But traders are already paring back forecasts for how many cuts the Fed will provide through the middle of next year.
In other dealings early Thursday, the U.S. dollar weakened against the Japanese yen, slipping to 154.46 from 154.62. The euro rose to $1.0740 from $1.0730.
U.S. benchmark crude oil gained 45 cents to $72.14 per barrel. Brent crude, the international standard, was up 55 cents at $75.47.
The price of bitcoin slipped to $75,780 after hitting an all-time high above $76,480 on Wednesday, according to CoinDesk. Trump has pledged to make the country "the crypto capital of the planet" and create a "strategic reserve" of bitcoin.
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AP Business Writer Stan Choe contributed to this report.
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