Despite the inability to maintain steady fixation, congenital nystagmus does not necessarily reduce visual acuity, that can be achieved during the foveation periods. The duration of the foveation period, but also the cycle-to-cycle variability of eye position and velocity during foveations play an important role. A quantitative relationship that relates visual acuity with foveation time and cycle-to-cycle variability of eye position during foveation has been previously proposed. In many infrared-oculographic and electro-oculographic eye position recordings of our database, a sinusoidal-like oscillation of the baseline was observed, on which the nystagmus waveforms lay. This oscillation may contribute to increase cycle-to-cycle variability during foveations. The aim of this work is to extract the baseline oscillation from the recordings and to verify its relationship with eye position variability during foveation. On the basis of the observations, the baseline oscillation was assumed to be sinusoidal, and was estimated (using a least mean square technique) from eye movement signals recorded during fixation intervals, at different gaze positions, from 20 patients affected by congenital nystagmus with low visual acuity. The average baseline oscillation amplitude was 1.31 degrees, while the average frequency was 0.34 Hz. Baseline oscillation amplitude was well correlated (with a coefficient of 0.66) to the standard deviations of eye-position during foveation, which in turn is connected to visual acuity.