  First, we investigate the static non-Abelian Kubo equation. We prove that it
does not possess finite energy solutions; thereby we establish that gauge
theories do not support hard thermal solitons. A similar argument shows that
"static" instantons are absent. In addition, we note that the static equations
reproduce the expected screening of the non-Abelian electric field by a gauge
invariant Debye mass m=gT sqrt((N+N_F/2)/3). Second, we derive the non-Abelian
Kubo equation from the composite effective action. This is achieved by showing
that the requirement of stationarity of the composite effective action is
equivalent, within a kinematical approximation scheme, to the condition of
gauge invariance for the generating functional of hard thermal loops.
