  For 3D reaction--diffusion equations, we study the problem of existence or
nonexistence of an inertial manifold that is normally hyperbolic or absolutely
normally hyperbolic. We present a system of two coupled equations with a cubic
nonlinearity which does not admit a normally hyperbolic inertial manifold. An
example separating the classes of such equations admitting an inertial manifold
and a normally hyperbolic inertial manifold is constructed. Similar questions
concerning absolutely normally hyperbolic inertial manifolds are discussed.
