The development of materials with large optical nonlinearities is a key to controlling the propagation of light beams by optical means. The control of light by light requires that photons can strongly interact. This is only possible in media where the optical properties of the materials, such as the refractive index, depend on the light intensity. The availability of appropriate materials for this purpose could revolutionize information technology again in a similar manner to the development of materials for semiconductor electronics.Optical materials with a sufficiently large intensity-dependent refractive index, which could play a similar role to silicon in electronics, have not yet been identified. This field is still at the stage of basic research, where strong efforts are devoted to an understanding of the fundamental relations between structure and optical nonlinearities. It is clear, however, that materials with a highly polarizable electron system are interesting candidates for achieving strong polarizations of the medium, which follow the electric field of the lightwave in a nonlinear manner. Therefore, organic materials with a delocalized n-electron system have found much interest and large nonlinearities of one-dimensional (1 D) conjugated polymers have been reported [l-111. As the optical properties of conjugated polymers are determined largely by the extent of electron delocalization, the corresponding conjugated oligomers have a key role in the study of the scaling of the linear and nonlinear optical properties with the size of the system. It will be seen that the size of the delocalized electron systems and electron correlation effects primarily determine the optical nonlinearities of oligomers.The emphasis of this chapter is on third-order nonlinearities, because they can lead to an intensity-dependent refractive index. The large potential of oligomers, such as to vary their chain lengths systematically, can be used to study third-order phenomena, especially to elucidate characteristic structure-property relationships. Second-order phenomena are the basis for frequency doubling and electro-optical processes. However, they require other chemical systems such as a combination of electron donors and acceptors in noncentrosymmetric structures, which will not be treated here.