It is well known that normal physiological tremor of the fingers and alpha rhythm in the EEG, may share a common frequency band in the region of 10 Hz; that these two characteristics may be in some way related as a function of their frequencies, is a hypothesis which needs to be tested, as one element in establishing the physiology of physiological tremor. Bilateral occipital EEGs and simultaneous measurements of acceleration from the terminal phalanx of the middle finger of both hands were recorded from eight subjects. The data were analysed to produce power spectral densities and coherence functions, the latter being used to reveal the presence or absence of frequency elements common to both signals. No evidence was found that would support a hypothesis that the two characteristics were in any way frequency related, from which it can be inferred that the tremor is not under central control. In addition, tremor of the right and left hands does not show a synchronous relationship.