Frohlich's concept of coherently excited long-wavelength electric vibrations in the 1011 to 1012-Hz region associated with metastable states with a very high dipole moment in biological membranes has been the basis for explaining the extraordinary high sensitivity of certain biological systems to extremely weak electromagnetic signals. In this model, long-range collective interactions within the membranes may lead to oscillatory biochemical reactions (e.g., enzyme-substrate interactions in the greater membrane of the brain.) The resulting slow chemical oscillation is connected to a corresponding electric vibration by means of the large dipole moments of reaction-activated enzymes. Thus a macroscopic oscillating polarization is built up, causing large regions to oscillate coherently in the 10 to 100-Hz region (e.g., EEG activity). The remaining (unscreened) polarization causes the system to exhibit a ferroelectric instability. The nonlinear kinetic equations describing the system are discussed. Extremely low frequency fields interact with the limit cycle oscillation, which is caused to collapse for certain frequencies and intensities of the stimulation. This leads to the onset of propagating pulses even for an extremely weak stimulation. There is increasing experimental evidence for the rather speculative predictions. Furthermore, correspondence between this model and nerve impulse-generating models has been established.