Saccades made between targets at optical infinity require both eyes to rotate by the same angle. Nevertheless, these saccades are consistently accompanied by transient vergence eye movements. Here we have investigated whether the dynamics of these vergence movements depend on the trajectory of the coincident conjugate movement, and whether moving the head during eye-head gaze shifts modifies vergence dynamics. In agreement with previous reports, saccades with more symmetric (i.e., "bell-shaped") conjugate velocity profiles were accompanied by stereotyped biphasic vergence transients (i.e., a divergence phase immediately followed by a convergence phase). However, we found that saccades with more asymmetric, oscillatory-like dynamics (characterized by a typical conjugate reacceleration of the eyes following the initial peak velocity) were systematically accompanied by more complex vergence movements that also exhibited oscillatory-like dynamics. These findings could be extended to conditions where the head was free to move: comparable conjugate and vergence oscillations were observed during head-restrained saccades and combined eye-head gaze shifts. The duration of the vergence oscillation increased with gaze shift amplitude, such that as many as four vergence phases (divergence-convergence-divergence-convergence) were recorded during 55 degrees gaze shifts (approximately 240 ms). To quantify these observations, we first determined whether conjugate and vergence peak velocities were systematically correlated. Conjugate peak velocity was linearly related to the peak velocity of the initial divergence phase for saccades and gaze shifts of all amplitudes, regardless of their dynamics. However, for more asymmetric saccades and gaze shifts, the subsequent convergence and divergence peak velocities were not correlated with either the initial peak conjugate velocity or the peak velocity of the conjugate reacceleration. Next, we determined that the duration of the different conjugate and vergence oscillation phases remained relatively constant across all saccades and gaze shifts, and that the conjugate and vergence profiles oscillated together at approximately 7.5-10 Hz. Using computer simulations, we show that a classic feed-forward model is unable to reproduce vergence oscillations based solely on peripheral mechanisms. Furthermore, we demonstrate that small modifications to the gain and delay of a simple feedback model for saccade generation can generate conjugate oscillations, and propose that such changes reflect the influence of lowered alertness on the tecto-reticular pathways. We conclude that peripheral mechanisms can only account for the initial divergence that accompanies all saccades, and that the conjugate and vergence oscillations observed during asymmetric movements arise centrally from an integrative binocular controller.