Physical analogies are used to develop ideas on the origin of spontaneous oscillations in the electrical activity of the human brain and on the variation in these oscillations that accompany changes of state and of type of activity. A possible functional role of such oscillations in the overall activity of the brain and mechanisms responsible for certain pathologies of brain activity are examined. Existing phenomenology and current hypotheses are used as a basis for suggesting that: 1) spontaneous rhythms on the electroencephalogram (EEG) are due to the interaction between a finite number of autogenerators (pacemakers) formed by the neuronal populations of thalamic nuclei and functional units in the cortex that exhibit the properties of a passive oscillatory loop; 2) because of its well-defined nonlinearity, the interaction between thalamic autogenerators of different natural frequency leads to the generation of a great variety of observed EEG patterns that accompany different types of brain activity (including responses to external disturbances), all of which is a consequence of recent advances in the theory of nonlinear oscillations that have led to the discovery of ``strange attractors''; 3) the subdivision in the brain of the pulsed flow of information into ``specific'' and ``nonspecific'', where the latter has a modifying influence on interactions between thalamic pacemakers and on the appearance of special multiperiodic patterns that are characteristic for different events, leads to a distributed fixation of long-term memory traces when the nonspecific and specific flows converge on a neuron memory substrate, and these traces can be read by a single characteristic multiperiodic pattern; and 4) the mechanism responsible for the appearance of paroxysmal discharges in certain specific types of epilepsy and the associated characteristic EEG phenomena (including frequency division) ensues from pathologically modified interaction between thalamic pacemakers and functional units in the cortex, which exhibits resonance properties.