1. We recorded abducens neurons, identified by electrical stimulation as internuclear neurons or motoneurons, in awake rabbits. The relationship of firing rate to eye movement was determined from responses during stable fixations, sinusoidal rotation in the light (0.05-0.8 Hz), and triangular optokinetic stimulation at 0.1 Hz. 2. All abducens neurons were excited during temporal movement of the ipsilateral eye. Temporal and nasal saccades were associated with bursts or pauses, respectively, in the firing rate. 3. Motoneurons and internuclear neurons are qualitatively indistinguishable. There was no significant quantitative difference between the phase and sensitivity of the two groups for 0.2-Hz sinusoidal rotation in the light. 4. On the basis of the response to stable eye positions, we determined static eye position sensitivity of the abducens neuron pool to be 8.2 +/- 2.5 (SD) spikes.s-1/0, with a static hysteresis of 8.9 spikes/s (1.14 +/- 0.37 degrees). 5. We determined apparent eye position sensitivity (k) and apparent eye velocity sensitivity (r) from the responses to sinusoidal rotation in the light. k increases and r decreases with stimulus frequency, which indicates that the simplest transfer function mediating conversion of abducens nucleus (VI) firing rate to eye position (E) has two poles and one zero. 6. The VI-->E relationship has an "amplitude nonlinearity," manifest as a tendency for k, r, and firing rate phase lead to decrease as eye movement amplitude increases at a fixed frequency. On a percentage basis, phase is less affected than are the sensitivities. The nonlinearity becomes less pronounced for stimulus amplitudes > 2.5 degrees, and consequently a linear model of the VI-->E transformation remains useful, provided that consideration is restricted to the appropriate range of stimulus/response amplitudes. 7. We determined time constants of the linear two-pole, one-zero transfer function from the variation of r/k versus stimulus frequency. The pole time constants were T1 = 3.4 s and T2 = 0.28 s, and the zero time constant (Tz) = 1.6 s. The magnitude of Tz was corroborated by measuring the time constant of the exponential decay in firing rate after step changes in eye position. This transient method yielded a Tz of 1.1 s. 8. The time constants of the VI-->E transfer function are roughly 10 times larger than those reported for the rhesus macaque. The difference is attributable to the reported 10-fold lower stiffness of the rabbit oculomotor plant, which may in turn relate to rabbits postulated lower degree of activation of extraocular muscles at any given position.(ABSTRACT TRUNCATED AT 400 WORDS)