We really know nothing about the boys' biological parents except that they've been dead for many years. Their mother died giving birth to Mokuba (Seto was 5), and their father in a car accident 3 years later (MOkuba was 3, Seto was 8). The boys had other living relatives, but none wanted to take them into custody, so they became wards of the state.

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I'm almost to Pegasus' Castle. I've got to be on my guard. His goons are everywhere, but they won't stop me. Nothing will. Mokuba's life's at stake and nothing's more important than my little brother. After our parents died, I promised I'd always take care of him, and I will. He's always looked up to me, and I won't disappoint him. Not now, not ever.--Seto Kaiba