The flavor composition of a dense gas of neutrinos changes in a
complicated fashion. This phenomenon, called collective effects, still
remains poorly understood. In the past decade, many insights into this
problem have been obtained based on an assumption of steady state
conditions. We will show that the steady state is unstable, and such
instability can arise at very high density. This may have major
implications for flavor oscillations in a supernova and the neutrino
mechanism of supernova explosions.