A singular perturbation problem for a reaction-di¤usion equation with a
nonlocal term is treated. We derive an interface equation which describes the dynamics
of internal layers in the intermediate time scale, i.e., in the time scale after the layers are
generated and before the interfaces are governed by the volume-preserving mean
curvature flow. The unique existence of solutions for the interface equation is demonstrated.
A continuum of equilibria for the interface equation are identified and the
stability of the equilibria is established. We rigorously prove that layer solutions of the
nonlocal reaction-di¤usion equation converge to solutions of the interface equation on a
finite time interval as the singular perturbation parameter tends to zero.