The isothermal, stationary and isochoric flow of a fluid of grade two between a pair of rotating eccentric spheres is investigated. The equations of motion of first and second order are formulated and solved for the first order only. However, the equation of second order indicates the presence of secondary flow. The stress distributions are computed and used to determine the resultant forces and torques acting on the stationary outer sphere. An important result for rheometry is that the resultant torques can be used to determine the coefficient of viscosity, while the resultant force in the direction of the axis of symmetry may be employed to determine the second normal stress difference.