We extend the application of the Z-scan experimental technique to determine free-carrier nonlinearities in the presence of bound electronic refraction and two-photon absorption. We employ this method, using picosecond pulses in CdTe, GaAs, and ZnTe at 1.06 m and in ZnSe at 1.06 and 0.53 Am, to measure the refractive-index change induced by two-photon-excited free carriers (coefficient ar,), the two-photon absorption coefficient 1, and the bound electronic nonlinear refractive index n2. The real and imaginary parts of the third-order susceptibility (i.e., n2 and 13, respectively) are determined by Z scans with low inputs, and the refraction from carriers generated by two-photon absorption (an effecitve fifth-order nonlinearity) is determined...