  In this paper, we introduce the notion of n-Hom-pre-Lie superalgebras. We
investigate the representation theory of n-Hom-pre-Lie superalgebras and we
give some related results and structures based on Rota-Baxter operators,
O-operators and Nijenhuis operators. Moreover, we study relationships between
n-Hom-pre-Lie superalgebras and its induced Hom-pre-Lie superalgebras. The same
procedure is applied for the representations of n- Hom-pre-Lie superalgebras.
