After being among the first to launch free schools in Stockholm, Gothenburg and Malmö, Greger Fjell and Gösta Rydell, also bought high schools in other areas and by 2011 their company (PPS Group) was in charge of 3600 pupils and had made a profit of 10 million kronor ($1.3m).
But they then sold part of their company (PPS Group) to a private equity firm, Riverside. Some of their profits left the country and the two contractors formed a new holding company based in both Sweden and Cyprus, Swedish news network SVT has reported.
The pair are accused of avoiding paying taxes in their own country as part of a complex financial deal.
When asked about the arrangement, Rydell told SVT it was "so complicated so I do not know if it is possible to explain”.
He said that he and his co-worker had at some stage considered moving to Cyprus, but that the plan was now off the table.
“If you are retired you should stay in Portugal, because the tax is apparently lower. I haven’t looked into this just read about it,” he added.
Both contractors are now being asked to repay overdue taxes in Sweden.
Sweden has led the world in encouraging businesses to set up schools after the first were set up in the 1990s and the system has long been praised by campaigners in other European countries, especially the UK.
The schools have attracted hundreds of millions of kronor from international private equity firms and venture capitalists, which have viewed the country’s privatised state sector as a worthwhile investment.
But the country’s school system is in focus following sliding school results in Sweden, which has slipped down the influential Programme for International Student Assessment (Pisa) league tables in recent years.
The current Social Democrat-Green coalition is reviewing the institutions and Prime Minister Stefan Löfven has warned against schools that are more focussed on making a profit than improving education for children.
Swedes are going to the polls again in March 2015, after a budget crisis caused the leader to call a snap election.