We present electronic-structure calculations for the isostructural (AuCu3-structure) series of intermetallic compounds ARh3 (A=Ac, Th, Pa, U, Np, Pu, Am, and Cm). The calculations were performed using both the scalar relativistic and the fully relativistic linear muffin-tin orbital (LMTO) method. Calculated cohesive and magnetic properties are compared with available experimental data. The onset of magnetism is discussed by means of a relativistic Stoner theory. The influence of the ligand states on the uranium 5f electrons is studied for the UM3 (M=Mo, Tc, Ru, Rh, Pd, and Ag) series of compounds. The localization of the 5f electrons in UPd3 as opposed to the itinerant 5f behavior for the earlier compounds (UMo3, UTc3 , URu3, and URh3) is explained in terms of the variation of the hybridization between 5f and ligand 4d states through the series.