When the energy of a pump wave is in resonance with the exciton creati
on energy, the electric susceptibility of a conjugated polymer in resp
onse to the probe wave is altered by the exciton gas. In this paper we
calculate the dependence of this change on the exciton populations by
the equation of motion (EOM) method. The magnitude of optical nonline
arity is also influenced by ambient temperature, by the extent of exci
ton wave functions, and by the strength of electron-electron interacti
on. All of these factors can be easily incorporated in the EOM approac
h systematically. Using the material parameters for polydiacetylene, t
he optical Ken coefficient n(2) obtained is about 10(-8) cm(2)/W, whic
h is close to experimental value, and is four orders of magnitude larg
er than the value in nonresonant pump experiments.