1. In the alert monkey, 74 neurons in the vestibular nuclei were investigated during sinusoidal rotation about a vertical axis at frequencies between 0.003 and 0.5 Hz. Phase and gain were determined by a fast Fourier analysis program. 2. Phase advance, relative to turntable velocity, was small between 0.05 and 0.5 Hz. At lower frequencies phase advance increased to 45 degrees at 0.007--0.02 Hz, and 90 degrees at 0.003--0.005 Hz. In agreement with the phase characteristics, a gain decrease of -3 dB was determined between 0.007 and 0.02 Hz. Assuming a linear system, time constants of 9.5, 11.9, and 24.5 s were calculated for three different monkeys. 3. Simultaneously recorded nystagmus exhibited similar time constants as the central vestibular neurons for each monkey. 4. Frequency responses of 11 neurons were recorded from the same monkeys while they were under general anesthesia and the time constants were reduced to 4--7 s. This is the range of time constants seen in the peripheral nerve. 5. The longer time constants in the alert state are due to an integration process, which provides a low-frequency compensation, and is thought to be achieved through a feedback loop involving the reticular formation. 6. In the alert and anesthetized state, monkeys were also exposed to velocity trapezoids. Time constants of decay of neuronal activity were in good agreement with the data obtained during sinusoidal stimulation. 7. A transfer function of the primary vestibular afferents is expanded to include the described low-frequency compensation found in central vestibular neurons in the alert animals.