Ab initio calculations have been carried out on the o-carborane cage (1,2-C2B10H12) With a carbene (-CH) or nitrene (-N) substituent at the 1-, 3-, or 9-position. When the carbene or nitrene is attached to the 1-position (carbon vertex), the singlet carbene is stabilized relative to the triplet. In contrast, when attached to the 3- or 9-position (boron vertex), the triplet is stabilized. Except for 1-CH-1,2-C2B10H11 (where the singlet-triplet splitting is small), all carboranylcarbenes and carboranylnitrenes considered have triplet ground states. The lowest-energy singlet state of the carboranylnitrene is the open-shell singlet when nitrogen is attached to the 3- or 9-position and closed-shell singlet when attached to the 1-position. All carboranylcarbenes are predicted to be bent (singlets, 108-114 degrees; triplets, 129-140 degrees). However, the triplet inversion stationary structure is nearly linear (179-180 degrees) and, for substitution at the 3- or 9-position, only 1.0 kcal/mol higher than the triplet minimum.