Determinism is a special property of some systems and is defined by its state-space behavior in which the trajectories in time never intersect. Whether or not determinism exists in brain activities is a question that may be resolved by analysis of the dynamical properties of the electroencephalogram (EEG) or magnetoencephalogram (MEG). We will show that even though there are strong nonstationarities in most brain behaviors, small epochs of deterministic dynamics can still be observed. We will also show that the local Lyapunov exponents are measures that can demonstrate smooth transitions into these deterministic states.