In Hong Kong, the Hang Seng surged 667.94 points or 3.15 percent to 21,889. 28.
The Nikkei 225 advanced by 396.68 points or 1.48 percent in Japan to close Tuesday at 27,224. 11.
The Australian All Ordinaries gained 61.80 points or 0.82 percent to 7,620. 70.
In New Zealand, the S&P NZX 50 climbed 26.94 points or 0.22 percent to 12,204. 69.
The U.S. dollar was higher on foreign exchange markets Tuesday. The euro fell to 1.0972 at the Sydney close. The British pound wilted to 1.3135. The Japanese yen weakened sharply to 1.2046. The Swiss franc fell to 0.9365.
The Canadian dollar fell to 1.2605, while the Australian dollar fell to 0.7386. The New Zealand dollar fell to 0.6574.
The Dow Jones Industrial Average went up 201.94 points, or 0.58%, over the night on Wall Street to close Monday at 34,552. 99.
The Standard and Poor's 500 fell by 1.94 points, or 0.040%, to 4,461. 18.
The Nasdaq Composite fell 55.38 points, or 0.40%, to 13,838. 46.