At 5 pm on Monday, the three Swedish IS women landed at Stockholm-Arlanda Airport, together with six of their children.
All have been in the Roj camp in northeastern Syria since the last IS stronghold fell two and a half years ago.
The women have been expelled from Kurdish autonomy for life since the authorities there, who assess that they pose a security threat, believe that there is insufficient evidence to prosecute.
Now they instead want Sweden to try women legally.
According to the Ministry of Foreign Affairs, Sweden has an obligation to receive Swedish citizens who cannot be prosecuted.
The social services, the Swedish Migration Agency and the police were on site at the airport to meet the women and children.
The prosecutor's office announced earlier on Monday that preliminary investigations have been launched against people returning from IS-controlled areas.
The authority does not currently want to comment on whether preliminary investigations have been initiated against any of the IS women who have now been deported to Sweden.
But according to sources to Swedish Radio Ekot, one or more of the women are suspected of war crimes.
The text is updated.