Nonlinear absorption coefficients have been calculated for certain direct-bandgap semiconductors at 0.694-microm, 1.06-microm, 1.318-microm, and 10.6-microm wavelengths and compared with experimental results. The second- order perturbation theories of Braunstein and Basov yield underestimates and overestimates, respectively, of the nonlinear absorption constants. The numerical values are dependent upon the use of appropriate effective band masses, dielectric constants, and electron spin degeneracy factors. However, the Keldysh model gives second-order absorption constants that are intermediate between the two perturbation calculations. Although the Keldysh model often underestimates the value, in general, it yields the estimate of the magnitude of the two-photon absorption coefficient. The one-photon band-edge absorption in GaAs and InSb is predicted surprisingly well by the Keldysh model.