  We extend the covariant GNS representation of Niculescu, Str\"oh and Zsid\'o
for C*-dynamical systems with time-evolution of the system (dynamics) a
homomorphism of C*-algebras, to any dynamical systems, where the dynamics is an
unital completely positive map. We give also an overview on its application to
the reversible dilation theory as formulated by B. Kummerer.
