The Ericksen theory of anisotropic fluids is examined with respect to its usefulness for describing the constitutive properties of real fluids. It is found that except in the limit of low shear rates, anisotropic effects may not be observed in simple laminar shearing flows or in helical flows, in both of which the behavior of these materials is indistinguishable from the predictions of the isotropic theory of simple fluids, and such flows do not suffice to determine uniquely all the material functions needed to describe other configurations. In unsteady flows, the theory as presently developed is limited to applications in which the fluid time constant is much smaller than the characteristic time of the flow field, i.e., to flows for which the Deborah number is sufficiently small. In these, the theory of simple fluids again appears to suffice with but the same exception.