IN THIS PAPER, WE GIVE A NEW COUPLED FIXED POINT THEOREM FOR A CLASS OF OPERATORS IN BANACH SPACES, USING THE TECHNIQUE OF MEASURE OF NON -COMPACTNESS AND DARBO, S FIXED POINT THEOREM.FURTHERMORE AS AN APPLICATION OF THIS RESULT, WE OBTAIN A THEOREM ON THE EXISTENCE OF SOLUTIONS FOR A SYSTEM OF NONLINEAR FUNCTIONAL INTEGRAL EQUATIONS.