  The aim of this paper is to extend Gerstenhaber formal deformations of
algebras to the case of Hom-Alternative and Hom-Malcev algebras. We construct
deformation cohomology groups in low dimensions.
  Using a composition construction, we give a procedure to provide deformations
of alternative algebras (resp. Malcev algebras) into Hom-alternative algebras
(resp. Hom-Malcev algebras). Then it is used to supply examples for which we
compute some cohomology invariants.
