  A subset $D\subseteq V_G$ is a dominating set of $G$ if every vertex in
$V_G\setminus D$ has a neighbor in $D$, while $D$ is a 2-dominating set of $G$
if every vertex belonging to $V_G\setminus D$ is joined by at least two edges
with a vertex or vertices in $D$. A graph $G$ is a $(2,2)$-dominated graph if
it has a pair $(D,D')$ of disjoint $2$-dominating sets of vertices of $G$. In
this paper we present two characterizations of minimal $(2,2)$-dominated
graphs.
