Abstract : A final addition is given to the experimental study of the band edge of CdTe. This consists of an attempt to obtain the best possible fit of the CdTe data with the theory of indirect interband and indirect exciton absorption. The failure of this theory to account for the data is examined in detail. A summary is also given of a theoretical study of the band edge in CdTe that is nearing completion. It was found that a quantitative fit of the experimental data can be provided by a mechanism involving the creation of a 'direct' exciton simultaneous with the absorption of one or two longitudinal-optical phonons. The theory is carried beyond a previous approximate treatment applied by Thomas, Hopfield, and co-workers (Phys. Rev. 119:570, (1960); J. Appl. Phys. Suppl. 32:2282, (1961)) to absorption edge studies in CdS and ZnO, with a resultant improvement in fitting the data.