  We study the dynamics of the one-dimensional $\varepsilon$-dependent
Cahn-Hilliard / Allen-Cahn equation within a neighborhood of an equilibrium of
$N$ transition layers, that in general does not conserve mass. Two different
settings are considered which differ in that, for the second, we impose a
mass-conservation constraint in place of one of the zero-mass flux boundary
conditions at $x=1$. Motivated by the study of Carr and Pego on the layered
metastable patterns of Allen-Cahn in [10], and by this of Bates and Xun in [5]
for the Cahn-Hilliard equation, we implement an $N$-dimensional, and a
mass-conservative $ N-1$-dimensional manifold respectively; therein, a
metastable state with $N$ transition layers is approximated. We then determine,
for both cases, the essential dynamics of the layers (ode systems with the
equations of motion), expressed in terms of local coordinates relative to the
manifold used. In particular, we estimate the spectrum of the linearized
Cahn-Hilliard / Allen-Cahn operator, and specify wide families of
$\varepsilon$-dependent weights $\delta(\varepsilon)$, $\mu(\varepsilon)$,
acting at each part of the operator, for which the dynamics are stable and rest
exponentially small in $\varepsilon$. Our analysis enlightens the role of mass
conservation in the classification of the general mixed problem into two main
categories where the solution has a profile close to Allen-Cahn, or, when the
mass is conserved, close to the Cahn-Hilliard solution.
