Let G be a connected graph. A subset is called duplex equitable dominating set if for each vertex ???? , there exists two vertices ???? ???? such that ???? dominates ????and ???? equitable dominates ????. The smallest cardinality of duplex equitable domination set is known as duplex equitable domination number and it is represented by A duplex equitable dominating set D of a graph G is non split duplex equitable domination set if the subgraph induced by the vertices in V-D is connected. The smallest number of non-split duplex equitable dominating set is known as non split duplex equitable domination number and is represented by ns????????( ). In this paper, we investigate the upper and lower bounds of and the exact values for some classes of graphs. Also we prove for any connected graph G, ⌈ ⌉ and find the relationship between and other domination parameters like χ, κ and ∆.