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The two-photon absorption coefficients (beta) and the third-order nonlinear susceptibilities (chi(3)) of several semiconductor nanoparticles (CdS, Cd(x)Ag(1-x)S, and core-shell CdS/Ag2S) that are confined and stabilized by random and block ionomers have been measured by nonlinear transmission and degenerate four-wave mixing techniques using 21 picosecond laser pulses at near-infrared spectral region. The imaginary part of the third-order nonlinear susceptibility that is related to the two-photon absorption coefficient was then calculated. The absorptive nonlinearity of the nanoparticles (2 approximately 9 nm) was found to be dependent on the particle size, composition and wavelength, i.e., larger CdS particles exhibit higher two-photon absorption coefficients and the presence of Ag improves two-photon absorption of CdS nanoparticles. The obtained two-photon absorption coefficients of nanoparticles corrected for their volume fraction in solution are significantly greater that those of corresponding bulk semiconductors.