Frozen solution electron paramagnetic resonance (EPR) spectra are reported for [(eta(4)-cod)Rh(mu-RNNNR)(2)-Ir(CO)(2)](+) (cod = 1,5-cyclooetadiene), [(PPh3)(CO)Rh(mu-RNNNR)(2)Ir(CO)(PPh3)](+) (R = p-tolyl) and [Tp'Ir-(CO)(PPh3)](+) (Tp' = hydrotris(3,5-dimethylpyrazolyl)borate). In the first spectrum, the Rh hyperfine coupling dominates and there are no significant quadrupolar effects. In the second spectrum, the low-field (g, and g,) features are 1:2:1 triplets rather than 1:1:1:1 quartets (I = 3/2 for Ir-191 and Ir-193), and in the third, the x and y features appear to be doublets. These anomalies result from the very large quadrupole moment for the iridium isotopes. This can be partially understood from a perturbation theory treatment, but quantitative simulations require direct matrix diagonalization and careful treatment of the problem, with respect to the orientation of the electron spin and nuclear spin quantization axes. The theoretical aspects of the calculations are presented, together with an interpretation of the results in terms of the electronic structures of the complexes.