The authors study the conditions under which the constitutive equations for fibre suspension flows are consistent with the second law of thermodynamics, and under which such flows are stable in the energetic sense. The model uses orientation tensors in the context of the following closure approximations: linear and quadratic closures, a rule due to Hinch and Leal, the smooth orthotropic closure rule of Cintra and Tucker, and the natural closure of Verleye and Dupret. It is shown that, with the linear closure approximations, the constitutive equations are consistent with the second law, and the flows are monotonically stable, provided the particle number does not exceed 35/2. The quadratic and natural closures are consistent and stable in two-dimensional case. The stability of Hinch-Leal closure cannot be established for arbitrary flows, whereas the rule of Cintra and Tucker is shown not to be consistent with the second law for arbitrary flows.