According to Danish law it's illegal to be married to more than one person, and this was brought into focus particularly in connection to the Iraqi interpreter who was given a residence permit in Denmark even though he had two wives.
Apparently he's not the only one. In response to a question by DPP's Peter Skaarup, Justice minister Lene Espersen says that in the years 2000-2006 there were 46 cases of polygamy. This is based on a report by the national police from last year.
In 17 cases a ruling was reached in the form of a sentence, warning or fine.
Source: Kristeligt Dagblad (Danish)