Eustathios' sons Pothos and Leo would go on to hold senior military commands, including the post of Domestic of the Schools (commander-in-chief). Another son, Romanos, is known only from his participation in the Battle of Achelous in 917. Leo Argyros married a daughter of Emperor Romanos I Lekapenos (r. 920–944), and was probably the grandfather or great-grandfather of Emperor Romanos III Argyros (r. 1028–1034).