[1] During the Spanish Civil War, he was the president of the Comité Nacionalista Español (CNE), a Cuban organization dedicated to the Carlist and Falangist ideologies of the Nationalist faction.

[2] At the conclusion of the war, he was awarded the Grand Cross of the Order of Isabella the Catholic by Francisco Franco for his services to Spain.

[3] The historian Allan Chase writes that Argüelles was a blue-blood landowner who was in charge of the CNE cell "A-1," alongside his friend José Ignacio Rivero Alonso, who headed the cell "R-1.

"[4] Argüelles and his son, Elicio Argüelles II, were good family friends of Ernest Hemingway, and met him at a Jai alai game.

[5] Argüelles owned the Frontón Jai Alai, the largest Jai Alai arena in Hanava.