Møgeltønder was formerly part of the German Empire. In the German Empire, the place was called Mögeltondern.
The place is now called Møgeltønder (Tønder-Møgeltønder) and belongs to Denmark.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Mögeltondern | German Empire | Tondern | before the Versailles Treaty |
| Møgeltønder | Denmark | Tønder | after the Versailles Treaty |
| Møgeltønder (Tønder-Møgeltønder) | Denmark | Sønderjylland | 1993 |