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For a vertex $v$ in a graph $G$, the set $N_2\left(v\right)$ consists of those vertices of $G$ whose distance from $v$ is 2. If a graph $G$ contains a set $S$ of vertices such that the sets $N_2\left(v\right)$, $v\in S$, form a partition of $V\left(G\right)$, then $G$ is called a $2$-step domination graph. We describe $2$-step domination graphs possessing some prescribed property. In addition, all $2$-step domination paths and cycles are determined.