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In this paper, we outline a suitable methodology for the analysis of nonstationary electrophysiological signals. The methodology is founded on a Bayesian approach to spectral estimation, which offers definite advantages in objectivity as compared to other approaches. The analysis of such signals is important in experimental paradigms where one is interested in tracking changes in spectral power or coherence. We describe how this methodology has been successfully applied to scalp EEG and deep brain local field potentials recorded from Parkinsonian patients, and used to deduce task related changes in power and coherence that are relevant to the understanding of the neural organisation of voluntary movement.