Alonso married the artist Ivonne Fauvety. Following the coup of 1976, and the disappearance of his daughter Paloma (born 25 July 1956) the following year, Alonso went into exile in Italy, and in 1979, he moved to Madrid. He returned to Argentina two years later. The Bienal de Pintura Paloma Alonso. named in her honor, is a 1990 joint initiative of Alonso and Teresa Nachman.