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The Banach contraction principle is the most famous fixed point theorem. Many authors presented some new results for contractions in partially ordered metric spaces. Fixed point theorems in modular spaces, generalizing the classical Banach fixed point theorem in metric spaces, have been studied extensively by many mathematicians. The aim of this paper is to determine some coupled fixed point theorems for nonlinear contractive mappings in the framework of a modular space endowed with a partial order. Our results are generalizations of the fixed point theorems due to M. Mursaleen, S.A. Mohiuddine and R.P. Agarwal.