Gremenzwald was formerly part of the German Empire. In the German Empire, the place was called Gremenzwald.
The place is now called Gaj-Grzmięca and belongs to Poland.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Gay-Gremenz | German Empire | Strasburg i. Westpr. | before the Versailles Treaty |
| Gaj-Grzemięca | Poland | Brodnica | after the Versailles Treaty |
| Gremenzwald | German Empire | Strasburg (Westpr.) | 1939 |
| Gaj-Grzmięca | Poland | Brodnica | 1945 |
| Gaj-Grzmięca | Poland | Toruń | 1992 |