Nielsen had five children, two of them illegitimate. He had already fathered a son, Carl August Nielsen, in January 1888, before he met Anne Marie. In 1912, an illegitimate daughter was born – Rachel Siegmann, about whom Anne Marie never learned. With his wife Nielsen had two daughters and a son. Irmelin, the elder daughter, studied music theory with her father and in December 1919 married Eggert Møller (1893–1978), a medical doctor who became a professor at the University of Copenhagen and director of the polyclinic at the National Hospital. The younger daughter Anne Marie, who graduated from the Copenhagen Academy of Arts, married the Hungarian violinist Emil Telmányi (1892–1988) in 1918; he contributed to the promotion of Nielsen's music, both as a violinist and a conductor. Nielsen's son, Hans Børge, was handicapped as a result of meningitis and spent most of his life away from the family. He died near Kolding in 1956.