  Effects of decoherence by wave packet separation on collective neutrino
oscillations in dense neutrino gases are considered. We estimate the length of
the wave packets of neutrinos produced in core collapse supernovae and the
expected neutrino coherence length, and then proceed to consider the
decoherence effects within the density matrix formalism of neutrino flavour
transitions. First, we demonstrate that for neutrino oscillations in vacuum the
decoherence effects are described by a damping term in the equation of motion
of the density matrix of a neutrino as a whole (as contrasted to that of the
fixed-momentum components of the neutrino density matrix). Next, we consider
neutrino oscillations in ordinary matter and dense neutrino backgrounds, both
in the adiabatic and non-adiabatic regimes. In the latter case we study two
specific models of adiabaticity violation -- one with short-term and another
with extended non-adiabaticity. It is demonstrated that, while in the adiabatic
case a damping term is present in the equation of motion of the neutrino
density matrix (just like in the vacuum oscillation case), no such term in
general appears in the non-adiabatic regime.
