  (Multiplicative) Hom-Lie-Yamaguti superalgebras which generalize Hom-Lie
supertriple systems (and subsequently ternary multiplicative Hom-Nambu
superalgebras) and Hom-Lie superalgebras in the same way as Lie-Yamaguti
superalgebras [Frac] generalize Lie supertriple systems and Lie superalgebras
are defined. We show that the category of (multiplicative) Hom-Lie-Yamaguti
superalgebras is closed under twisting by self-morphisms. Construction of some
examples of Hom-Lie-Yamaguti superalgebras is given. The notion of an
$n^{th}-$derived (binary) Hom-superalgebras is extended to the one of an
$n^{th}-$derived binary-ternary Hom-superalgebras and it is shown that the
category of Hom-Lie-Yamaguti superalgebras is closed under the process of
taking $n^{th}-$ derived Hom-superalgebras.
