  We analyze ill-defined pinch singularities characteristic of out of
equilibrium thermal field theories. We identify two mechanisms that eliminate
pinching even at the single self-energy insertion approximation to the
propagator: the first is based on the vanishing of phase space at the singular
point (threshold effect). It is effective in QED with a massive electron and a
massless photon. In massless QCD, this mechanism fails, but the pinches cancel
owing to the second mechanism, i.e., owing to the spinor/tensor structure of
the single self-energy insertion contribution to the propagator. The
constraints imposed on distribution functions are very reasonable.
