For a given eye position, firing rates of abducens neurons (ABNs) generally (Mays et al. 1984), and lateral rectus (LR) motoneurons (MNs) in particular (Gamlin et al. 1989a), are higher in converged gaze than when convergence is relaxed, whereas LR and medial rectus (MR) muscle forces are slightly lower (Miller et al. 2002). Here, we confirm this finding for ABNs, report a similarly paradoxical finding for neurons in the MR subdivision of the oculomotor nucleus (MRNs), and, for the first time, simultaneously confirm the opposing sides of these paradoxes by recording physiological LR and MR forces. Four trained rhesus monkeys with binocular eye coils and custom muscle force transducers on the horizontal recti of one eye fixated near and far targets, making conjugate saccades and symmetric and asymmetric vergence movements of 16-27°. Consistent with earlier findings, we found in 44 ABNs that the slope of the rate-position relationship for symmetric vergence (kV) was lower than that for conjugate movement (kC) at distance, i.e., mean kV/kC = 0.50, which implies stronger LR innervation in convergence. We also found in 39 MRNs that mean kV/kC = 1.53, implying stronger MR innervation in convergence as well. Despite there being stronger innervation in convergence at a given eye position, we found both LR and MR muscle forces to be slightly lower in convergence, -0.40 and -0.20 g, respectively. We conclude that the relationship of ensemble MN activity to total oculorotary muscle force is different in converged gaze than when convergence is relaxed. We conjecture that LRMNs with kV < kC and MRMNs with kV > kC innervate muscle fibers that are weak, have mechanical coupling that attenuates their effective oculorotary force, or serve some nonoculorotary, regulatory function. © 2011 the American Physiological Society.