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The object of this article is to investigate the Dirichlet averages of the generalized multi–index Mittag–Leffler functions introduced by Saxena and Nishimoto [23, 24]. Representationsof such relations are obtained in terms of Riemann–Liouville integrals and hypergeometricfunctions of several variables. Some interesting special cases of the established results as-sociated with generalized Mittag–Leffler functions due to Srivastava and Tomovski [32] andmulti–index Mittag–Leffler functions due to Kiryakova [12] are deduced. Certain resultsgiven earlier by Kilbaset al.[8] also follow as special cases of our findings.