The gynarchy possibly could be passed down through generations.

It is also sometimes called a gynarchy, a gynocracy, a gynecocracy, or a gynocentric society.

Gynecocracy, gynaecocracy, gynocracy, gyneocracy, and gynarchy generally mean 'government by women over women and men'.

In 351, Zagig renounced the title of Despot, leaving the Gynarchy of Hardby to choose another Despotrix to rule the city.

According to Paul J. Smith, it was to this kind of gynarchy that "Kong ascribed...the general collapse of society" and Kong believed that men in Jiangnan tended to "forfeit...authority to women".