A wave of buying in technology stocks sent Wall Street shares higher, paring some of Friday's sharp losses.
Concern remains about the global impact of any US slowdown
While concerns continue about the state of the US economy, investors were cheered by strong preliminary results from US computer giant IBM.
The main Dow Jones index was up 172 points, or 1.36% at 12,778.1. On Friday it had closed down 247 points.
Europe's main share indexes finished ahead on Monday, but Hong Kong's Hang Seng ended down nearly 400 points.
The UK's main FTSE 100 index closed up 13.7 points at 6,215.7, while Germany's Dax had added 14.07 points, and France's Cac had gained 32.1 points.
Sydney's main ASX 200 index ended Monday down 13.5 points at 5,980, while trading in Tokyo was closed for a public holiday.
Shares on Wall Street fell heavily on Friday because of continuing concerns about the state of the US economy.
In addition to investment bank Goldman Sachs predicting a recession this year, confidence among US investors was hit further last week by weak trading updates from American Express and Tiffany.
US Federal Reserve boss Ben Bernanke also warned that the 2008 outlook for the US economy has worsened.
The slowdown in the US economy centres on the sharp slump in the housing market, which sparked last August's global credit squeeze.
Many of the leading US banks have revealed multi-million dollar bad debts in the so-called sub-prime mortgage sector, and this has made them much less willing to lend to each other, as well as to businesses and consumers.
Investors will be keeping a close watch on the fourth-quarter numbers and full-year financial results from Citigroup and Merrill Lynch expected later this week.
Both banks have suffered hugely as investments linked to sub-prime home loans have collapsed.