  In this paper, we consider some hyperbolic variants of the mass conserving
Allen-Cahn equation, which is a nonlocal reaction-diffusion equation,
introduced (as a simpler alternative to the Cahn-Hilliard equation) to describe
phase separation in binary mixtures. In particular, we focus our attention on
the metastable dynamics of some solutions to the equation in a bounded interval
of the real line with homogeneous Neumann boundary conditions. It is shown that
the evolution of profiles with $N+1$ transition layers is very slow and we
derive a system of ODEs, which describes the exponentially slow motion of the
layers. A comparison with the classical Allen-Cahn and Cahn-Hilliard equations
and theirs hyperbolic variations is also performed.
