  In the category of semisimple Hopf algebras the Hopf kernels introduced by
Andruskiewitsch and Devoto in \cite{AD} coincide with kernels of representation
as introduced in \cite{Bker}. Some new results concerning the normality of
kernels are also presented. It is proven that the property for Hopf algebras to
have all kernels normal Hopf subalgebras is a self dual property.
