The magneto-optical Kerr spectra of several transition-metal-An alloys are investigated theoretically, on the basis of relativistic energy-band theory in the framework of the local-spin-density-functional theory. Calculated Ken spectra are presented for the artificial compounds FeAu and MnAu, and also for the ordered XAU4 (X::: V, Cl', Mn) compounds. The theoretical Ken spectra of FeAu correspond in shape to the experimental spectra, but the calculated Kerr effect is bigger than the experimental one. For the XAU4 compounds a modest Kerr angle of-0.4" to-0.5° at, 1.7eV is predicted. The XAU4 compounds are predicted to display a huge Kerr anisotropy, which is purely a magnetocrystaIline anisotropy effect.