Mølmark was formerly part of the German Empire. In the German Empire, the place was called Möllmark.
The place is now called Mølmark and belongs to Denmark.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Möllmark | German Empire | Sonderburg | before the Versailles Treaty |
| Mølmark | Denmark | Sønderborg | after the Versailles Treaty |
| Mølmark | Denmark | Sønderjylland | 1993 |