In the previous work, Part I; [1], the steady flow of an incompressible Oldroyd 8-constant fluid in the annular region between two concentric spheres is investigated up to the second-order approximation. Hence, the normalized second-order velocity field, V shows to be ) 1 ( ) 1 ( ) 1 ( ) 1 ( 3 ) 2 ( ) 2 ( ) 1 ( ) 0 ( ˆ ˆ sin ); ( ˆ ˆ V U r r O W W V                           U U The leading velocity term represents the Newtonian flow in the  -direction, while the first-order term denoted by the stream–function ) , r ( ) 1 (   , produces a secondary flow field that divides the flow region into four parts symmetric about the z-axis which is the axis of rotation. The second-order approximation gives a viscoelastic contribution ) , r ( W ) 2 (  in the  -direction.  is the retardation time parameter. The present work is devoted to the solution of the third-order approximation of the same problem treated in [1]. The solution produces a stream–function ) , r ( ) 3 (   which is being a secondary flow field divides the domain of flow into two similar regions symmetric about an axis perpendicular to the axis of rotation. The streamlines . const ) , r ( ) 3 (    are sketched for Maxwell, Oldroyd-B and Oldroyd 8-constant model fluids; respectively. The results show that the distribution of flow for these fields are mainly affected by the values of their elastic parameters.