  The aim of this paper is to study the metastable properties of the solutions
to a hyperbolic relaxation of the classic Cahn-Hilliard equation in one space
dimension, subject to either Neumann or Dirichlet boundary conditions. To
perform this goal, we make use of an "energy approach", already proposed for
various evolution PDEs, including the Allen-Cahn and the Cahn-Hilliard
equations. In particular, we shall prove that certain solutions maintain a {\it
$N$-transition layer structure} for a very long time, thus proving their
metastable dynamics. More precisely, we will show that, for an exponentially
long time, such solutions are very close to piecewise constant functions
assuming only the minimal points of the potential, with a finitely number of
transition points, which move with an exponentially small velocity.
