While Japan's benchmark index rose slightly after a three day holiday, markets elsewhere struggled to hold onto Monday's gains.
The Nikkei 225 in Tokyo rose 0.1 percent to 14,423.87. Hong Kong's Hang Seng fell 0.3 percent to 23,189.17. South Korea's Kospi fell 0.6 percent to 2,001.54. Australia's S&P/ASX 200 was nearly unchanged at 5,249.80.
World stock markets rose Monday after Lawrence Summers, who had been the leading candidate to replace Fed chairman Ben Bernanke, pulled his name from consideration. Markets responded positively because Summers was thought to favor quickly reducing the Fed's stimulus program, which has been a boon for stock markets.
On Wall Street, the Dow Jones industrial average rose 0.8 percent, to close at 15,494.78. The Standard & Poor's 500 rose 0.6 percent, to 1,697.60. The Nasdaq composite fell 0.1 percent, to 3,717.85.
Benchmark oil for October delivery fell 71 cents to $105.88 per barrel in electronic trading on the New York Mercantile Exchange. The contract fell $1.62 to lose at $106.59 a barrel on the Nymex on Monday.
In currencies, the euro fell to $1.3330 from $1.3335 late Monday. The dollar rose to 99.22 yen from 99.10 yen.
___
Follow Pamela Sampson on Twitter at http://twitter.com/pamelasampson