  In this paper, we focus on the duo ring property via quasinilpotent elements
which gives a new kind of generalizations of commutativity. We call this kind
of ring qnil-duo. Firstly, some properties of quasinilpotents in a ring are
provided. Then the set of quasinilpotents is applied to the duo property of
rings, in this perspective, we introduce and study right (resp., left) qnil-duo
rings. We show that this concept is not left-right symmetric. Among others it
is proved that if the Hurwitz series ring $H(R; \alpha)$ is right qnil-duo,
then $R$ is right qnil-duo. Every right qnil-duo ring is abelian. A right
qnil-duo exchange ring has stable range 1.
