Muespach-le-Haut was formerly part of the German Empire. In the German Empire, the place was called Obermüspach.
The place is now called Muespach-le-Haut and belongs to France.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Obermüspach | German Empire | Altkirch | before the Versailles Treaty |
| Obermuespach | France | Haut-Rhin | after the Versailles Treaty |
| Obermüspach | German Empire | Altkirch | 1940 |
| Muespach-le-Haut | France | Haut-Rhin | 1945 |
| Muespach-le-Haut | France | Haut-Rhin | 1993 |