  The present paper deals with autonomous integral equations with infinite
delay via dynamical system approach. Existence, local exponential attractivity,
and other properties of center manifold are established by means of the
variation-of-constants formula in the phase space that is obtained in a
previous paper \cite{mur}. Furthermore, we prove a stability reduction
principle by which the stability of an autonomous integral equation is implied
by that of an ordinary differential equation which we call the "central
equation".
