Gáspár was the son of Lázár Kuun de Osdola but his mother is unknown. The date and place of his birth have not been found.
His wife was Erzsébet Gyulay de Valka. They were married, but the date and place have not been found. Their three known children were Gotthárd (?-?), István (?-1659) and Erzsébet (?-?).
| Attribute | Date | Description | Details | Source | Multimedia | Notes |
|---|---|---|---|---|---|---|
| Nobility Title | Belsõ-Szolnok vármegye fõispánja (comes of Belső-Szolnok County) |