The contributions of nonlinear absorption processes to laser-induced damage of three selected groups of transparent dielectrics were investigated. The studied materials were irradiated and non-irradiated fused silica, doped and undoped fluorozirconate glass and cubic zirconia stabilized with yttria. The laser-induced damage thresholds, prebreakdown transmission, and nonlinear absorption processes were studied for several specimens of each group. Experimental measurements were performed at wavelengths of 1064 nm and 532 nm using nanosecond and picosecond Nd:YAG laser pulses. In the irradiated fused silica and fluorozirconate glasses, we found that there is a correlation between the damage thresholds at wavelength λ and the linear absorption of the studied specimens at λ/2. In other words, the laser-induced breakdown is related to the probability of all possible two-photon transitions. The results are found to be in excellent agreement with a proposed two-photon-initiated electron avalanche breakdown model. In this model, the initial "seed" electrons for the formation of an avalanche are produced by two-photon excitations of E' centers and metallic impurity levels which are located within the bandgaps of irradiated Si02 and fluorozirconate glasses, respectively. Once the initial electrons are liberated in the conduction band, a highly absorbing plasma is formed by avalanche impact ionization. The resultant heating causes optical damage. In cubic zirconia, we present direct experimental evidence that significant energy is deposited in the samples at wavelength 532 nm prior to electron avalanche formation. The mechanism is found to be due to formation of color centers (F+ or F° centers) by the two-photon absorption process. The presence of these centers was directly shown by transmission measurements. The two-photon absorption (2PA) process was independently investigated and 2PA coefficients obtained. The accumulated effects of the induced centers on the nonlinear absorption measurements were also considered and the 2PA coefficients were measured using short pulses where this effect is negligible. At room temperature, the color centers slowly diffuse out of the irradiated region. The density of these centers was monitored as a function of time. The initial distribution of the centers was assumed to have a Gaussian profile. For this model the diffusion equation was solved exactly and the diffusion constant obtained.