Canada's benchmark S&P/TSX rose 13.63 points, or 0.16%, to 8,257.60.
London's stock, bond, foreign exchange, and energy markets were closed for the May Day holiday. Other major European stock markets finished higher.
Germany's DAX index rose 22.44 points, or 0.56%, to 4,007.65. There was little reaction to a report German PMI rose to 55.3 on April from 54.1 in March.
In Paris, the CAC 40 index was up 31.2 points, or 0.85%, to 3,705.48, with some help from a report French API rose to 53.5 in April from 53.2 in March.
Japan's equity market is closed for Golden Week -- trading will resume on Thursday, May 6.
In Hong Kong, the Hang Seng index gained 7.66 points, or 0.06%, to close at 11,950.62 as sentiment continued to be weighed down by China woes and possible rate hikes in the U.S.