It was founded in October 1929 in A Coruña by Santiago Casares Quiroga and Antón Vilar Ponte with the participation of the Irmandades da Fala.
Represented by Casares Quiroga, it was a signatory of the Pact of San Sebastián.
The Radicals left the Galician Republican Federation following the proclamation of the Republic although the FRG continued to exist until 1932.
Santiago Casares Quiroga was a cabinet minister in republican governments between 1931 and 1933.
In 1932, the Argentine section of ORGA led by Ramón Suárez Picallo participated in the foundation of the Partido Galeguista led by Castelao.