Non-Newtonian fluid flow between a pair of rotating cylinders with non-equal size rolls and/or non-equal speed of the rolls is studied theoretically for the power-law fluids at the isothermal condition, using the bipolar cylindrical coordinates which could satisfy the exact boundary conditions. A theoretical analysis of the velocity, pressure and shear stress distributions in the flow field is given by solving equations of continuity and motion applying the lubrication approximation. The processing parameters such as volumetric flow rate and total power required to drive the rolls are calculated and presented in terms of the geometrical and kinematical parameters of the asymmetric calendering systems.