A subset $D$ of $V(G)$ is called an equitable dominating set of a graph $G$ if for every $v\in(V-D)$, there exists a vertex $u\in D$ such that $uv\in E(G)$ and $|\deg(u)-\deg(v)|\leq 1$. The minimum cardinality of such a dominating set is denoted by $\gamma_e(G)$ and is called equitable domination number of $G$. In this paper we introduce the equitable edge domination and equitable edge domatic number in a graph, exact value for the some standard graphs bounds and some interesting results are obtained.