Third-order nonlinear optical susceptibilities of sigma-conjugated one-dimensional polymers have been calculated in a tight-binding model by taking account of the formation of excitons due to long-range Coulomb interactions. The spectrum of third-harmonic generation (THG) exhibits peaks due to excitons as well as unbound electron-hole states, in contrast to the linear absorption spectrum which is dominated by the lowest exciton state. The results are in excellent agreement with recent experiments in polysilanes not only for THG but also for linear absorption, two-photon absorption, and electroabsorption in a mutually consistent way.