This thesis provides an extensive study of the first molecular hyperpolarizability b of charge-transfer chromophores using hyper-Rayleigh scattering (HRS). The charge-transfer chromophores used in present work involve the tricyanohydrofuran¡]TCF¡^group as an electron acceptor, and/or thiophene in the pi-electron bridge. TCF is a very strong electron acceptor and thiophene greatly lowers the resonance energy. Their presence significantly increases the beta value of the chromophore, therefore enhancing potentials in applications. In hyper-Rayleigh scattering experiments, the laser radiation with tunable wavelengths is used as an excitation source for measuring the frequency dependence of beta. The experiment shows beta exhibiting a significant dispersion in the two-photon resonance region. Using the linear absorption spectrum in coordination with theory, we show that it is possible to use Kramers-Kronig (K-K) transform to reproduce the experimental beta value in the two-photon resonance region. The K-K approach provides an extension to the conventional Oudar-Chemla equation, which is invalid in the spectral region in which two-photon resonance occurs. Using the new approach, it is shown that reliable values of intrinsic hyperpolarizabilities beta_zero of charge-transfer chromophores can be extracted. The coordination of beta_zero with molecular structure provides one with an insight for the origin of the enhancement of the first molecular hyperpolarizability of charge-transfer chromophores. This thesis examines the variation of beta_zero with molecular structure. The same technique is also applied to a dendrimer that has charge-transfer nonlinear optical chromophores incorporated in the dendritic structure. The measured frequency dependent hyperpolarizability of the dendrimer is compared with that calculated from the linear absorption spectrum by the KK transform technique. The intrinsic hyperpolarizability beta_zero of the dendrimer obtained is compared with that of the single chromophore having a structure similar to that incorporated in the dendrimer. The comparison shows that the 3D dendritic structure is effective in reducing the interaction between chromophores by providing sufficient space between them, hence avoiding the possibility of aggregation formation due to attractive interactions between chromophores. The topic of two-photon fluorescence (TPF), which is related to HRS, is also investigated. The intensity of TPF is generally proportional to the square of the incident excitation intensity. Careful measurements of the TPF intensity of a nonlinear optical chromophore in conjunction with required auxiliary parameters have been used as a technique for determining the two-photon absorption cross-section. The TPF intensity measurement carried out in this thesis uses a variety of intensities. At low intensity excitation, the TPF intensity follows the usual quadratic intensity law (QIL), whereas deviations from the QIL are observed at higher incident intensities. The observation of similar lineshape associated with one- and two-photon fluorescence spectra suggests a 3-level model for the description of TPF excited by the incident intensity at various strengths. It is shown that by fitting the observed TPF intensity to an equation developed from the three-level model, it is possible to deduce the two-photon absorption cross section of the nonlinear optical chromophore in solution. The new technique developed using the three-level model is tested on a Rhodamine B/Chloroform solution. The two-photon absorption cross-section obtained by using the new technique is found in agreement with that reported in the literature. Having demonstrated the suitability of the new technique, it is used to determine the two-photon absorption cross-section of a novel nonlinear optical chromophore. The two-photon absorption cross-section using the new technique is then compared with that obtained by the nonlinear transmittance method. The two results are in good agreement, indicating the applicability of the new technique. The new technique is more convenient than the conventional low excitation TPF method as it does not require various auxiliary parameters, some of them are difficult to obtain. The second harmonic generation (SHG) of a chromophore/polymer film which is optically poled by using a coherent superposition of a fundamental and its second harmonic beams. The growth rate of the SHG intensity is found to be proportional to the fourth power of the incident intensity of the fundamental beam, and the plateau intensity SHG is proportional to the square of the incident intensity. These observations are not in agreement with the published theory. While the reason for disagreement is yet to be clarified, the information obtained is useful for the development of nonlinear optical devices.