Last week Baxter International, the Deerfield, Illinois healthcare company, announced it would buy Gambro AB, the privately held Swedish dialysis product maker for about $4 billion.

For Gambro, which is owned by Sweden-based private equity funds Investor AB and EQT, the opportunity to join Baxter and form the world’s second-largest dialysis company was too good to pass. Growth at Gambro in recent years has slowed down due to price competition and a slumping European economy. For Baxter, which in 2011 had revenue of nearly $14 billion and a pile of cash overseas, it was a strategic opportunity to deploy the capital. But for EQT and Investor AB, the two private equity funds that own Gambro, it was another highly profitable deal that the Swedish dealmakers helped engineer.

In an environment in which dealmakers that also are long-term global investors are in short supply, Swedish private equity funds find themselves in great demand. “We’ve always been investors for the long term, avoiding the cyclicals and focusing on telecommunications, transformational IT and healthcare,” says Thomas von Koch, a founding partner of EQT, which manages more than $18 billion in assets.

Although Sweden’s involvement in global M&As and private equity pales next to the U.S. and even the U.K., its importance within Europe has grown significantly — especially as most of its neighbors face economic uncertainty and forecasts of slow growth ahead. In 2011, the flow of investment funds into Sweden amounted to $5.6 billion or 14.1 percent of the total funds flowing into Europe, according to data compiled by EVCA, the Brussels-based trade group representing European private equity and venture capital. Just five years ago in 2007, the $4.6 billion of funds that went into Sweden accounted for only 5.7 percent of the total.

The flow of capital into 368 Swedish companies in 2011 rose to $8.7 billion or 7.4 percent of the total invested in European companies. In 2007, the flow of private equity into 478 Swedish companies was $2.1 billion, less than 1 percent of the total into European companies.

At a time when the euro zone is near collapse, beset by unstable currencies, conflicting laws and regulations, and unpredictable markets, Sweden — in spite of its size and geographical location — has emerged as one of the continent’s safe havens.