Creutzfeldt-Jakob disease is a rare, neurological, dementing disorder characterised by periodic sharp waves in the electroencephalogram (EEG). Non-linear analysis of these EEG changes may provide insight into the abnormal dynamics of cortical neural networks in this disorder. Babloyantz et al. have suggested that the periodic sharp waves reflect low-dimensional chaotic dynamics in the brain. In the present study this hypothesis was re-examined using newly developed techniques for non-linear time series analysis. We analysed the EEG of a patient with autopsy-proven Creutzfeldt-Jakob disease using the method of non-linear forecasting as introduced by Sugihara and May, and we tested for non-linearity with amplitude-adjusted, phase-randomised surrogate data. Two epochs with generalised periodic sharp waves showed clear evidence for non-linearity. These epochs could be predicted better and further ahead in time than most of the irregular background activity. Testing against cycle-randomised surrogate data and close inspection of the periodograms showed that the non-linearity of the periodic sharp waves may be better explained by quasi-periodicity than by low-dimensional chaos. The EEG further displayed at least one example of a sudden, large qualitative change in the dynamics, highly suggestive of a bifurcation. The presence of quasi-periodicity and bifurcations strongly argues for the use of a non-linear model to describe the EEG in Creutzfeldt-Jakob disease.