Polarized oscillatory magnetoabsorption spectra of exciton formation transitions in InSb have been measured under high resolution at liquid helium temperature. An unstrained high‐mobility sample 5 &mgr; thick and magnetic fields up to 39.1 kgauss were used. Diffraction grating dispersion for the region 3.7<&lgr;<6.0 &mgr; made possible a resolution of 1−7×10−4ev and the determination of absorption maxima to ±5×10−5ev. Sixteen minima were resolved withE⊥Bfor a field of only 5.0 kgauss. The initial interpretation of the detailed spectra obtained involved fitting theoretical spectra calculated from the theories of Kane, Luttinger, and Elliott‐Loudon in order to account for band nonparabolicities, valence band degeneracy effects, and exciton binding energies, respectively. The results experimentally established the light‐hole nonparabolicity, the valence band degeneracy effects for low magnetic quantum numbers, and the existence of high‐field excitons in InSb.