Citizenship for Children of Icelandic Citizens, born 1964-1982
If a child is born before July 1, 1982 to a mother who is an Icelandic citizen and who is married to the father, who is a foreign citizen, then the child does not automatically acquire Icelandic citizenship at birth. The Icelandic Nationality Act has been amended, however, to include a provision that allows applicants born between July 1, 1964, and June 30, 1982, to declare their right to Icelandic citizenship. Note that applications connected to Icelandic citizenship are only available in Icelandic.
See more at the Directorate of Immigration.