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 Ω 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 (α ,β ,φ ) . 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 ψ 2 , due to the effect of the inertia, which describes the planar secondary flow field has been properly obtained