According to Friston, brain dynamics can be modelled as a large ensemble of coupled nonlinear dynamical subsystems with unstable and transient dynamics. In the present study, two predictions from this model (the existence of nonlinear synchronization between macroscopic field potentials and itinerant nonlinear dynamics) were investigated. The dependence of nonlinearity on the method of measuring brain activity (EEG vs. MEG) was also investigated. Dataset I consisted of 10 MEG recordings in 10 healthy subjects. Dataset II consisted of simultaneously recorded MEG (126 channels) and EEG (19 channels) in 5 healthy subjects. Nonlinear coupling was assessed with the synchronization likelihood S and dynamic itinerancy with the synchronization entropy Hs. Significance was assessed with a bootstrap procedure ("surrogate data testing"), comparing S and Hs with their distribution under the null hypothesis of stationary, linear dynamics. Significant nonlinear synchronization was detected in 14 of 15 subjects. The nonlinear dynamics were associated with a high index of itinerant behaviour. Nonlinear interdependence was significantly more apparent in MEG data than EEG. Synchronous oscillations in MEG and EEG recordings contain a significant nonlinear component that exhibits characteristics of unstable and itinerant behaviour. These findings are in line with Friston's proposal that the brain can be conceived as a large ensemble of coupled nonlinear dynamical subsystems with labile and unstable dynamics. The spatial scale and physical properties of MEG acquisition may increase the sensitivity of the data to underlying nonlinear structure.