Concurrent activation of muscles on opposite sides of joints is a common phenomenon. In simple planar mechanical systems, it is easy to identify such an electromyographic pattern as co-contraction of agonist and antagonist muscles. In complex 3-D systems such as the lumbar spine, it is more difficult to precisely identify whether EMG recordings represent co-contraction. Qualitative definitions of antagonist muscles emphasize that their actions wholly oppose the action of the prime movers. The qualitative definition of antagonist muscles was used to formulate a mathematical requirement for there to be co-contraction of agonists and antagonists. It was shown that the definition of co-contraction implies muscle activity beyond what is required to maintain equilibrium. The method was illustrated by classifying EMG recordings made of the lumbar region musculature during tasks involving combined torso extension and axial twisting loads. The method, which identified muscle activity in excess of that required to maintain static equilibrium, could be used to identify conditions in which muscle activation is required for something other than merely maintaining moment equilibrium.