In 1960 Ericksen [1] introduced a simple theory of anisotropic fluids. This theory differs from the classical theory of fluids in that the deformation of the material is no longer solely described by the usual vector displacement field but requires in addition the specification of a further vector field di, termed the director. Moreover, corresponding to this increased kinematic flexibility new types of stress, body force and inertia are introduced. Leslie [2], adopting the conservation laws of [1], formulated constitutive equations similar to those considered by Ericksen and discussed the thermodynamical restrictions imposed by the Clausius–Duhem inequality. Here we shall consider the case in which at each point the director is constrained to remain a unit vector. Then the usual interpretation is to regard di as indicating a single preferred direction in the material (see for example [3]). It is thought that the physical applications of this theory are likely to lie in such areas as polymeric fluids and suspensions.