  The purpose of this paper is to study Hom-Lie superalgebras, that is a
superspace with a bracket for which the superJacobi identity is twisted by a
homomorphism. This class is a particular case of $\Gamma$-graded quasi-Lie
algebras introduced by Larsson and Silvestrov. In this paper, we characterize
Hom-Lie admissible superalgebras and provide a construction theorem from which
we derive a one parameter family of Hom-Lie superalgebras deforming the
orthosymplectic Lie superalgebra. Also, we prove a $\mathbb{Z}_2$-graded
version of a Hartwig-Larsson-Silvestrov Theorem which leads us to a
construction of a q-deformed Witt superalgebra.
