We consider the hyperbolic relaxation of the viscous Cahn-Hilliard equation epsilon phi(tt) + phi(t) - Delta(delta phi(t) - Delta phi + g(phi)) = 0, (0.1) in a bounded domain of R-d with smooth boundary when subject to Neumann boundary conditions, and on rectangular domains when subject to periodic boundary conditions. The space dimension is d=1, 2 or 3, but it is required delta = epsilon = 0 when d = 2or 3; delta being the viscosity parameter. The constant e is an element of (0, 1] is a relaxation parameter, phi is the order parameter and g : R -> R is a nonlinear function. This equationmodels the early stages of spinodal decomposition in certain glasses. Assuming that e is dominated from above by delta when d = 2 or 3, we construct a family of exponential attractors for Eq. (0.1) which converges as (epsilon, delta) goes to (0, delta(0)), for any delta(0) is an element of [0, 1], with respect to a metric that depends only on epsilon, improving previous results where thismetric also depends on delta. Then we introduce two change of variables and corresponding problems, in the case of rectangular domains and d = 1 or 2 only. First, we set (phi) over tilde (t) = phi(root epsilon t) and we rewrite Eq. (0.1) in the variables ((phi) over tilde, (phi) over tilde (t)). We show that there exist an integer n, independent of both epsilon and delta, a value 0 < <(epsilon)over tilde>(0) (n) <= 1 and an inertial manifold of dimension n, for either epsilon is an element of (0, (epsilon) over tilde (0)] and delta = 2 root epsilon or is an element of (0, (epsilon) over tilde (0)] and delta is an element of [0, 3 epsilon]. Then, we prove the existence of an inertial manifold of dimension that depends on e, but is independent of d and., for any fixed epsilon is an element of (0, (eta-2)(2)] and every delta is an element of[epsilon, (2-eta)root epsilon], for an arbitrary eta is an element of (1, 2). Next, we showthe existence of an inertialmanifold of dimension that depends on epsilon and eta, but is independent of delta, for any fixed epsilon is an element of (0, 1/(2+eta)(2)] and every delta is an element of[(2 + eta) root epsilon, 1], where eta > 0 is arbitrary chosen. Moreover, we show the continuity of the inertial manifolds at delta = delta(0), for any delta(0) is an element of [0, (2 - eta)root epsilon] boolean OR [(2 + eta root epsilon, 1]. Second, we set phi(t) = -(2 epsilon)-1(I - delta Delta)phi + epsilon(-1/2)v and we rewrite Eq. (0.1) in the variables (phi, v). Then, we prove the existence of an inertial manifold of dimension that depends on delta, but is independent of epsilon, for any fixed delta is an element of (0, 1] and every epsilon is an element of (0, 3/16 delta(2)]. In addition, we prove the convergence of the inertial manifolds when epsilon -> 0(+).