Markets in the United States are closed on Monday for the Labour Day holiday there, but others have risen on hopes the US economy can avoid slipping back into recession.
The FTSE 100 in London closed up 0.20% at a four-month high of 5439.
The DAX index in Frankfurt rose 0.30%, to finish at 6155.
The CAC-40 in Paris also rose 0.30%, to close at 3685 points.
Earlier, the Nikkei index in Tokyo ended on 9,301, up 187 points. The Hang Seng index in Hong Kong finished 21,355, up 384 points.
Across the Tasman, the Australian 200 Index rose 34 points, or 0.75%, at 4576.
The NZX 50 rose 36 points, or just over 1%, to 3143 on turnover of $102 million.
At 8.28am on Tuesday, the New Zealand dollar was trading at 72.28 US cents, 78.87 Australian cents, 46.97 pence, 60.90 yen and 0.5617 euro. The Trade Weighted Index was at 67.08.
Brent crude oil was trading at $US76.87 per barrel and gold was trading at $US1249.40 per ounce.