A possible role of selforganizing processes in brain function and development is discussed. It is argued that such processes are necessary in the light of plasticity and adaptability. Using examples from physics and chemistry as illustration, general properties and prerequisites of selforganization are stated. Recent developments in the mathematics of nonlinear dynamic systems are described and the concept of 'deterministic chaos' is explained. The brain meets all requirements for selforganizing processes to occur. Evidence for the role of selforganization in the brain is sought in spatially periodic activity patterns and intrinsic organization in the mammalian cortex. Background EEG activity and changes therein during epileptic seizures and sleep are discussed in terms of nonlinear chaotic dynamics.