  We investigate a scenario in which neutrinos are coupled to a pseudoscalar
degree of freedom $\ph$ and where decays $\nu_1 \to \nu_2+\ph$ and inverse
decays are the responsible mechanism for obtaining equilibrium. In this context
we discuss the implication of the invisible neutrino decay on the
neutrino-pseudoscalar coupling constant and the neutrino lifetime. Assuming the
realistic scenario of a thermal background of neutrinos and pseudoscalar we
update the bound on the (off-diagonal) neutrino-pseudoscalar coupling constant
to $g<2.6\times10^{-13}$ and the bound on the neutrino lifetime to
$\tau<1\times10^{13}\,\rm{s}$. Furthermore we confirm analytically that kinetic
equilibrium is delayed by two Lorentz $\ga$--factors -- one for time dilation
of the (decaying) neutrino lifetime and one from the opening angle. We have
also confirmed this behavior numerically.
