  In this paper, we give some basic properties of the generalized derivation
algebra ${\rm GDer}(L)$ of a Hom-Lie superalgebra $L$. In particular, we prove
that ${\rm GDer}(L) = {\rm QDer}(L) + {\rm QC}(L)$, the sum of the
quasiderivation algebra and the quasicentroid. We also prove that ${\rm
QDer}(L)$ can be embedded as derivations in a larger Hom-Lie superalgebra.
