European stocks generally advanced while Asian markets were mixed, with Chinese shares falling sharply.
Markets in the US and the UK are closed for holidays.
In Europe, the Stoxx Europe 600 gained 0.3% to 244.79, led by auto makers and technology-sector firms.
Daimler shares rose 1.7% and software giant SAP climbed 1.5%, as the German DAX added 0.3% to 5964.33.
Spain's Ibex 35 shed 0.7% to 9359.40 after Fitch Ratings cut Spain's sovereign-debt rating to double-A-plus from triple-A on Friday.
In Paris, the CAC-40 edged down 0.2% to 3507.56.
Chinese shares fell sharply as investors moved away from property companies after the State Council said it has approved a plan to gradually reform the country's real-estate tax system.
Other Asian markets were mixed, concluding a month that saw steep declines in regional indexes.
Japan's Nikkei Stock Average edged up 0.1% to 9768.70 but was down 12% for the month. Hong Kong's Hang Seng Index fell fractionally, down 1.52 points to 19,765.19, leaving it down more than 6% for the month.
Australia's S&P/ASX 200 slipped 0.6% to 4429.67, while Korea's Kospi climbed 1.1% to 1641.25 and Taiwan's Taiex gained 1.1% to 7373.98. All three indexes ended down for the month.
Commodities: Oil up
Crude futures made tentative gains in thin trading as the dollar weakened against a basket of major currencies.
In electronic trading, the front-month July contract in New York was 46USc higher at $US74.43 a barrel. The front-month July Brent contract on London's ICE futures exchange was up 63USc at $US74.65 a barrel.
Currencies: Euro, dollar up
The euro gained ground in exceptionally thin trading, with euro-zone's debt problems still dominant. The euro lost as much as 9.1% versus the dollar in May, and 13.2% against the yen.
The euro was at $US1.2282, from $US1.2270 late on Friday. The dollar was at ¥91.27, up from ¥90.92, while the euro was at ¥112.10, up from ¥111.68.
The UK pound was at $US1.4536, from $US1.4462.
Nevil Gibson
Tue, 01 Jun 2010