The purpose of this paper is to study Sabinin algebras of Hom-type. It is shown that Lie, Malcev, Bol and other algebras of Hom-type are naturally Sabinin algebras of Hom-type. To this end, we provide a general key construction that establish a relationship between identities of some class of Hom-algebras and ordinary algebras. Moreover, we discuss a new concept of Hom-bialgebra, in relation with universal enveloping Hom-algebras. A study based on primitive elements is provided. * FPU Grant from the Ministerio de Educación, Cultura y Deporte in Spain. Research project MTM2013-45588-C3-3-P set of operations µ i : A ⊗n i → A. We mean by a Hom-algebra an algebra together with a homomorphism.

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