The theory of optical absorption due to transitions between a valence band and a hydrogen-like local level associated with a conduction band is modified to permit an arbitrary power-law dependence of energy on the magnitude of the wave-vector of carriers in the valence band. The observed absorption for photon energies below 1.6 eV in the ferromagnetic semiconductor CdCr2Se4 is discussed in terms of a combination of two types of terms. The first type of absorption is due to transitions to a local level from a band with two branches, in each of which there is an energy region with a width of 0.28 eV or more beginning 0.10–0.16 eV from the band edge, in which the energy measured from some origin near but not necessarily equal to the band-edge is approximately proportional to (wave-vector)(13). The second type of absorption has a dependence on photon energy ħω of the form (ħω − E3)2, where E3 is a threshold energy probably connected with indirect transitions between bands as suggested by Sakai, Sugano and Okabe. After constraints on parameters appearing in the theory are imposed by use of results of these authors and of Shepherd, it is found that curves of Harbeke and Lehmann on optical absorption in CdCr2Se4 at 4.2, 78, 130 and 298 K in the photon-energy range 1.14–1.42 eV can be fitted to a mean accuracy of 3%, using an average of 3.75 adjustable parameters for each curve. The strength of the indirect band-to-band absorption does not have the temperature dependence expected for phonon-assisted indirect band-to-band transitions, but can be described by a term independent of temperature plus another term proportional to the square of the deviation of the magnetization from saturation. The fitting of the absorption curves requires that the ratio of the widths of the two branches of the bands varies from about 1.6 at low temperatures to 1.35 at 298 K and that the total width of the bands involved is less than 1 eV.