Several methods have been developed and used to characterize the narrow gap semiconductors Hg^_xCdxTe (HgCdTe) (0.20<x<0.32) and InSb both in the presence of CO2 laser radiation and in the dark. The results have allowed the determination of certain band parameters including the fundamental energy bandgap Eg which is directly related to x, the mole fraction of Cd. In the dark, characterization of several different samples of HgCdTe and InSb were carried out by analyzing the temperature dependence of the Hall coefficient and the magnetic field positions of the magnetophonon extrema from which their x-values were determined. The quality of the magnetophonon spectra is also shown to be related to the inhomogeneity Ax of the HgCdTe samples. One-photon magneto-absorption (OPMA) spectra have been obtained for x ~ 0.2 samples of p-HgCdTe thin films and n-HgCdTe bulk samples. Analysis of the OPMA transition energies allows the x-value to be determined to within « ±0.001. A method is also discussed which can be used to estimate the sample inhomogeneity Ax. Nonlinear optical properties of semiconductors are not only scientifically interesting to study, but are also proving to be technologically important as various nonlinear optical devices are being developed. One of the most valuable …