Quadrupedal animals moving on arboreal substrates face unique challenges to maintain stability. The torque generated by the limbs around the long axis of a branch during locomotion may clarify how the animals remain stable on arboreal supports. We sought to determine what strategy gray short-tailed opossums (Monodelphis domestica) use to exert torque and avoid toppling. The opossums moved across a branch trackway about half the diameter of their bodies. Part of the trackway was instrumented to measure substrate reaction forces and torque around the long axis of the branch. Kinematic analysis was used to estimate the center of pressure of the manus and pes; from center of pressure and vertical and mediolateral forces, the torque generated by substrate reaction forces versus muscular effort could be determined. Forelimbs generated significantly greater torque than hindlimbs, which is probably explained by the greater weight-bearing role of the forelimbs. Fore- and hindlimbs generated torque in opposite directions because contralateral fore- and hindlimbs typically contacted the branch. Torque generated by muscular effort, however, was often in the same direction in both fore- and hindlimbs. The muscle-generated torque is likely the result of mediolateral movement of the center of mass caused by mediolateral undulation of the torso. These results bear an important implication for the study of arboreal locomotion: center of mass dynamics are at least as important as static positions. M. domestica is a good representative for a primitive mammal, and comparisons with arboreal specialists will shed light on how proficient arboreal locomotion evolved.