The electronic structure, magnetism as well as the excited-state properties such as the optical and x-ray magnetic circular dichroism (XMCD) spectra of the Heusler alloys Co₂TiSn and Co₂ZrSn were investigated theoretically from first principles using the fully relativistic Dirac LMTO band structure method. The origin of the XMCD spectra at the Co L_2,3 edges in the compounds is examined. Densities of valence states, orbital and spin magnetic moments as well as optical spectra are analyzed and discussed. The calculated results are compared with the available experimental data.