The influence of the higher-conduction-band set G15c on the strength, linear/circular dichroism, and anisotropy of the ultrafast nonlinear refractive index coefficient (n2) is calculated across the transparent spectral region below the fundamental absorption edge for the zinc-blend semiconductors GaAs and InSb. The anisotropy is due entirely to the effects of the higher bands. For GaAs, at the two-photon band edge, and for linearly polarized light, n2 is predicted to vary by 55% as the crystal orientation is altered relative to the polarization direction. Even larger variations are expected at longer wavelengths. The far lower predicted anisotropy of InSb is consistent with the approximate formula for the strength of the anisotropy coefficient in terms of the ratio of the fundamental to the higher band gap discussed previously for two-photon absorption. The influence of such n2 anisotropy on propagation in both one-beam and two-beam configurations is discussed. The anisotropy of the optical-switching figure of merit is also evaluated. At frequencies just below the band edge the figure is found to be greatest for radiation linearly polarized parallel to the  crystallographic direction; just above the half-band gap and at lower frequencies  linear polarization or any circular polarization is favored. © 1995 The American Physical Society.