2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65466We continue the investigation of noncommutative cumulants. In this paper various characterizations of noncommutative Gaussian random variables are proved.14 pages, AMS-LaTeX; many corrections according to the referee; to appear in Prob Th Rel FieldsCombinatoricsOperator Algebras46L53; 05A18text