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In this paper we approximate common fixed points of nearly asymptotically nonexpansive mappings under modified S P-iteration process in the setting of CAT(k) spaces and establish strong and Δ-convergence theorems. Our results generalize and improve the corresponding known results of the existing literature. Keywords: Δ-convergence, Modified SP-iteration process, Nearly asymptotically nonexpansive mapping, Common fixed point, CAT(k) space, Mathematics Subject Classification: 47H09, 47H10