Converxencia XXI tries to provide solutions from a centrist point of view, which could help define the real needs of Galician society, which was plunged into a severe economic and social crisis around the time of the party's formation.

Founded in May 2009 by its later elected First Secretary, Carlos Vázquez Padín, Converxencia XXI started contacts with other European organisations.

The party entered into an early expansion stage, building up its militancy mostly via compromised citizens who share their ideological Liberal-Democrat and Reform basis.

Converxencia XXI presented signatures and won the right to participate in all Galicia territory, having the best election result in its history and consolidating itself as the country's second Galician political force.

The party's earliest achievements involved the foundation of the first internationally homologated Galician Think Tank, known as GALIDEM, within the European Liberal Forum.