  The relation between two versions of so called non-equilibrium statistical
operator method (NESOM), NESOM-1 due to Zubarev (1961) and NESOM-2 due to
Zubarev and Kalashnikov (1970), is considered. It is proved that, once the
balance equations of NESOM-2 are satisfied, those of NESOM-1 will be satisfied
with the same set of the macro-parameters. The proof uses the convexity-type
inequalities, and does not involve any assumptions additional to the rationales
behind NESOM. However, converse statement cannot be proved within this
technique. An extension of the proof to overall equivalence of the two
nonequilibrium ensembles is discussed. This arXiv publication is dedicated to
the memory of Dmitrii Nikolaevich Zubarev
