For a given position of the eye in the orbit, most abducens motoneurons (LRMNs) fire at higher rates in converged gaze than when convergence is relaxed, implying that lateral rectus (LR) muscle force will be higher for a given eye position in convergence. If medial rectus (MR) muscle force balances LR force, it too would be higher in convergence, that is, LRMN recording studies predict horizontal rectus co-contraction in convergence. Three trained rhesus monkeys with binocular eye coils and custom muscle force transducers (MFTs) on LR and MR of one eye alternately fixated near (approximately 7 cm) and far (200 cm) targets with vergence movements of 20–30°. Tonic muscle forces were also measured during conjugate fixation of far targets over a 30 × 30° field. MFT characteristics and effects on oculomotility were assessed. Contrary to predictions, we found small (<1 g) decreases in both LR and MR forces in convergence, for those gaze positions that were used in the brain stem recording studies. This missing LR forceparadox (higher LRMN firing rates in convergence but lower LR forces) suggests that motoneurons or muscle fibers contribute differently to oculorotary forces in converged and unconverged states, violating the final common path hypothesis. The absence of MR co-contraction is consistent with, and supports, the missing LR force finding. Resolution of the missing LR force paradox might involve nonlinear interactions among muscle fibers, mechanical specialization of muscle fibers and other articulations of the peripheral oculomotor apparatus, or extranuclear contributions to muscle innervation.