The exchange coupling of Ullman’s nitroxide biradicals, bis[2,2’-(1-oxy-3-oxido-4,4,5,5-tetramethyldihydro-1H-imidazolyl)] (1) and bis[2,2’-(1-oxy-4,4,5,5-tetramethyldihydro-1H-imidazolyl)] (2), has been determined by performing ab initio calculations followed by a specific configuration interaction on model compounds where the methyl groups have been substituted by hydrogen atoms, C1 and C2, respectively. The analysis of the dependence of the coupling on the conformation angle between each nitroxide moiety shows that even in the perpendicular structure the singlet state is found below the triplet. The calculated singlet-triplet gaps for the experimental value of the twist angle, -364 cm(-1) for C1 and -175 cm(-1) for C2, are in very good agreement with recent experimental results for 1 and 2.