Suppression of 5-25 Hz oscillations have been observed in MT+ during pursuit eye movements, suggesting oscillations that play a role in oculomotor control and/or the integration of extraretinal signals during pursuit. The amplitude of these rhythms appears to covary with head-centred eye position, but an alternative is that they depend on a velocity signal that lags the movement of the eyes. To investigate, we explored how alpha and beta amplitude changes related to ongoing eye movement depended on pursuit at different eccentricities. The results revealed largely identical patterns of modulation in the alpha and beta amplitude, irrespective of the eccentricity at which the pursuit eye movement was performed. The signals we measured therefore do not depend on head-centred position. A second experiment was designed to investigate whether the alpha and beta oscillations depended on the direction of pursuit, as opposed to just speed. We found no evidence that alpha or beta oscillations depended on direction, but there was a significant effect of eye speed on the magnitude of the beta suppression. This suggests distinct functional roles for alpha and beta suppression in pursuit behaviour.