  We prove global existence and uniqueness of solutions to a Cahn-Hilliard
system with nonlinear viscosity terms and nonlinear dynamic boundary
conditions. The problem is highly nonlinear, characterized by four
nonlinearities and two separate diffusive terms, all acting in the interior of
the domain or on its boundary. Through a suitable approximation of the problem
based on abstract theory of doubly nonlinear evolution equations, existence and
uniqueness of solutions are proved using compactness and monotonicity
arguments. The asymptotic behaviour of the solutions as the the diffusion
operator on the boundary vanishes is also shown.
