In this paper, Hom-Jordan and Hom-alternative bimodules are introduced. It is shown that Jordan and alternative bimodules are twisted via endomorphisms into Hom-Jordan and Homalternative bimodules respectively. Some relations between Hom-associative bimodules, Hom-Jordan and Hom-alternative bimodules are given.

In this paper, some results on representations of Hom-Leibniz algebras are found. Specifically the adjoint representation and trivial representation of Hom-Leibniz algebras are studied in detail. Deformations and central extensions of Hom-Leibniz algebras are also studied as applications.