  We introduce the class of split regular Hom-Lie superalgebras as the natural
extension of the one of split Hom-Lie algebras and Lie superalgebras, and study
its structure by showing that an arbitrary split regular Hom-Lie superalgebra
${\frak L}$ is of the form ${\frak L} = U + \sum_j I_j$ with $U$ a linear
subspace of a maximal abelian graded subalgebra $H$ and any $I_j$ a well
described (split) ideal of ${\frak L}$ satisfying $[I_j,I_k] = 0$ if $j \neq
k$. Under certain conditions, the simplicity of ${\frak L}$ is characterized
and it is shown that ${\frak L}$ is the direct sum of the family of its simple
ideals.
