  We study the non-abelian Hopf cohomology theory of Radford products with
coefficients in a comodule algebra. We show that these sets can be expressed in
terms of the non-abelian Hopf cohomology theory of each factor of the Radford
product. We write down an exact sequence relating these objects. This allows to
compute explicitly the non-abelian Hopf cohomology sets in large classes of
examples.
