Theoretical values are obtained for the thermal conductivity and the viscosity of a dense fluid of perfectly rough elastic spheres, on the basis of simple assumptions about the pair distribution functions. In this fluid angular momentum may be transferred from the bulk motion of the fluid to the rotations of the individual spheres. The rate of this transfer is given by an anti-symmetric component in the pressure tensor, and involves a coefficient of ‘rotational viscosity’, analogous to the shear viscosity arising from the symmetric component. The thermal conductivity is found to be twice as great as that for perfectly smooth spheres, while the viscosities involve the moment of inertia of the spheres as well as their mass and radius.