The study of the Non-Linear flow of a viscoelastic second-order fluid in the annular region between two eccentric spheres is investigated. This flow is created by considering the inner sphere to rotate with angular velocity about the axis passing through the centers of two spheres, the z-axis, while the outer sphere is kept at rest using the Bispherical coordinates . The equations of motions of second order fluid using retarded motion approximation including inertia term are formulated and the particular solution of the modified planar second-order equation of motion which including inertia term is obtained. A modified second-order stream function , due to the effect of the inertia, which describes the planar secondary flow field has been properly obtained