  The paper gives a comprehensive study of Inertial Manifolds for hyperbolic
relaxations of an abstract semilinear parabolic equation in a Hilbert space. A
new scheme of constructing Inertial Manifolds for such type of problems is
suggested and optimal spectral gap conditions which guarantee their existence
are established. Moreover, the dependence of the constructed manifolds on the
relaxation parameter in the case of the parabolic singular limit is also
studied.
