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Co/Cu multilayer nanowires fabricated in an array using anodized aluminium oxide (AAO) template has been investigated. Experimental conditions are optimized to fabricate Co/Cu multilayer systems with fixed Cu and variable Co layer thicknesses. Magnetization reversal mode is found to depend on the Co layer thickness. A transition occurs from coherent rotation to a combination of coherent and curling rotation at around t(Co) = 60 nm with increasing t(Co). The reversal modes have been investigated using the magnetic hysteresis loops measured at room temperature for Co/Cu nanowires placed at various angles between the directions of the nanowire axis and external fields using a vibrating sample magnetometer. The magnetic easy axis changes from the direction perpendicular to nanowires to that parallel to the nanowires at around t(Co) = 60 nm, indicating a change in the magnetization reversal mode. The reversal mode for the nanowires with thin disk-shaped Co layers is of a coherent rotation type, while that for long rod-shaped Co layers can be explained by a combination of coherent rotation and a curling mode.