  We calculate the damping rate $\gamma_l$ for longitudinal gluons with zero
momentum in finite high temperature QCD and show that some of its contributing
terms are infrared divergent. This is in contrast with the expectation that
this damping rate is to be equal to the corresponding one $\gamma_t$ for
transverse gluons which is known to be finite. Our calculation was motivated by
the fact that similar divergent terms occur when we calculated in a previous
work $\gamma_t$ to order $ p^2$, p being the momentum of the gluon. After we
present our results, we briefly discuss them.
