Let k be a field, H a Hopf algebra with a bijective antipode, A an associative algebra with identity on which H coacts in such a way that A is a right H-comodule algebra. We will give sufficient conditions for the category of relative (A , H)-Hopf modules to be semisimple; i.e.,
completely reducible. We recover a result of Ida Doraiswamy on semisimplicity of the category of rational (A, G)-modules, where G is a linear connected algebraic group acting rationally on a finitely generated commutative algebra A.