Abstract The analysis of structure and texture changes in cold-deformed copper by asymmetric rolling with different coefficient of rolls speed asymmetry R (R=2–4), was shown in recent paper. The results were compared to ones obtained for cold rolled copper with equal speed of both rolls (R=1). It was found that the application of asymmetric rolling conditions results in a greater strain hardening than in the case of the classical rolling process (R=1). The results have revealed that increase of the asymmetry coefficient R value, causes presence of higher fraction of high angle boundaries in as-deformed material structure, suggesting the possibility of occurrence of thermally activated processes of structure recovery or mechanical fragmentation of grains. Texture analysis has shown that application of rolling speed asymmetry results in a significant sharpening of the deformation texture (maximum ODF values were twice higher than for normally rolled samples (R=1)). In addition, for the variant with the greatest coefficient of rolling speed asymmetry (R=4), obtained deformation texture was characterized by a relatively low fraction of the typical rolling texture components (the Cu, the Bs, and the S), and significantly increased fraction of the shear texture components.