Let $G = (V, E)$ be a graph. A subset $D \subseteq V$ is said to be a dominating set of $G$ if every vertex in $V - D$ is adjacent to some vertex in $D$. The cardinality of a minimum dominating set $D$ is called the domination number of and is denoted by $\gamma(G)$. A subset $D$ of $V$ is called duplex equitable dominating set if for every vertex $v \in V - D$, there exists two vertices $u_1, u_2 \in D$ such that $u_1$ dominates $v$ and $u_2$ equitable dominates $v$. The minimum cardinality of duplex equitable dominating set is called duplex equitable domination number and it is denoted by $\gamma_{de}(G)$. In this paper, we obtain some results on Duplex Equitable domination number of a graph. we found the best possible upper and lower bounds for $\gamma_{de}$, characterize the graphs satisfies these bounds, obtained $\gamma_{de}$ number for some standard graphs and found relationship between other domination parameters like $\chi$, $\delta$ and $\Delta$.