The relationship between the ensemble average stress in a dilute suspension of spheres and the imposed rate of strain and rotation is derived for a general linear flow of a suspension in a second-order fluid. In a Newtonian fluid, the particulate phase only contributes to the stress via the shear viscosity; the contribution takes the form of a stresslet, the symmetric first moment of the force distribution on the surface of a suspended particle. In a second-order fluid, the interactions of the particles and polymers contribute to the stress in three ways: (1) the particle-induced fluid velocity disturbance alters the polymer stress in the fluid; (2) the polymer stresses exerted on the particle contribute to the particle's stresslet; (3) the non-Newtonian nature of the fluid changes the pressure and velocity field, thereby modifying the Newtonian contributions to the particle stresslet. The particle contributions Psi(P)(l) and Psi(P)(2) to the first and second normal stress differences are related to the corresponding stress differences (Psi(0)(1) and Psi(0)(2)) for the suspending fluid by Psi(P)(1) = (5/2)phi Psi(0)(1) and Psi(P)(2) = (75/28)phi Psi(0)(2) - (5/28)phi Psi(0)(1), where phi is the particle volume fraction. (c) 2006 Elsevier B.V. All rights reserved.