Band structures of β’-NiAl and CoAl have been calculated to interpret the experimental optical spectra. The optical transitions of both compounds are calculated as direct interband transitions including electric-dipole matrix elements between the eigenstates of the ground state of the system. All of the structures found in the optical spectra of both compounds involve states with some Ni or Co d character in both the initial and the final states. The overall agreement is good between the calculated spectrum and the optical data for β’-NiAl. For β’-CoAl there is qualitative agreement but some discrepancy for the energy positions and the intensities of the structures. A self-energy correction for the excitation spectrum has been used for β’-CoAl to improve the agreement.