Horizontal vergence eye movements are movements in opposite directions used to change fixation between far and near targets. The occurrence of a saccade during vergence causes vergence velocity to be transiently enhanced. The goal of this study was to test in the monkey the previously described Multiply Model (Zee et al. 1992) that holds that, in humans, the speeding of vergence during a saccade may be the result of the disinhibition of a subgroup of vergence-related neurons by the saccadic omnipause neurons (OPNs). In agreement with the Multiply Model: 1) the onset of the enhancement was closely related to saccadic onset, and thus linked to the onset of the OPN pause; 2) the magnitude of the vergence velocity enhancement was strongly dependent on saccade-vergence timing. Contrary to the Multiply Model: 1) the peak of the vergence velocity enhancement was dependent on saccadic peak velocity; 2) the dependence on saccadic peak velocity was not the indirect result of a dependence on saccadic duration and therefore on the duration of the OPN pause; 3) the decline of the vergence enhancement, identified by the time of the peak of the enhancement velocity, occurred too early to be linked to the end of the OPN pause; 4) vergence enhancement had a saccadic-like peak-velocity/size main sequence. Overall, the evidence is incompatible with the OPN Multiply hypothesis of vergence enhancement. Alternative models are described in an accompanying paper.