The Swedish firms are among 340 international companies that have been looked at by the International Consortium of Investigative Journalists (ICIJ).
It says it has seen leaked confidential documents suggesting that complicated accounting and legal arrangements have made it possible for major brands and companies to move their profits to Luxembourg in order to pay lower tax rates.
The tax arrangements of Swedish private equity firms Nordic Capital, IK Investment Partners and EQT have also been questioned.
A team of more than 80 journalists from 26 countries looked at documents dating from 2002 – 2010.
"The fact that this has come out, I believe will accelerate the work in the OECD [Organisation for Economic Co-operation and Development],” said Tomas Algotsson, Head of Sweden’s Tax Agency.
"It is a further confirmation of the use of different countries' tax rules to avoid tax”.
Tax laws were tightened in Sweden in 2009 and 2013.
The ICIJ said that Luxembourg was still a “magical fairyland” for corporations seeking to "drastically reduce tax bills".