The well-posedness of the equations governing the flow of fiber suspensions is studied. The fluid is assumed to be Newtonian and incompressible, and the presence of fibers is accounted for through the use of second- and fourth-order orientation tensors, which model the effects of the orientation of fibers in an averaged sense. The fourth-order orientation tensor is expressed in terms of the second-order tensor through various closure relations. It is shown that the linear closure relation leads to anomalous behavior, in that the rest state of the fluid is unstable, in the sense of Liapounov, for certain ranges of the fiber particle number. No such anomalies arise in the case of quadratic and hybrid closure relations. For the quadratic closure relation, it is shown that a unique solution exists locally in time for small data.