In this talk we will study the transference of algebraic structures through contractions. In particular, it is well known that in the case of algebras, in general, contractions don't preserve the associative law for the product; obtaining a more sophisticated structures: A_\infty-algebras. But until now, nothing was known if the original structure was a Hopf Algebra. Therefore, we will give an alternative notion to the concept of A_\infty-Hopf algebra (introduced by Prof. R. Umble and Prof. S. Saneblidze) using techniques of Perturbation Theory.