The signs of the Leslie viscosities alpha(2) and alpha(3) for rod-like and disc-like molecules in the uniaxial nematic phase are discussed using a dynamic molecular mean field theory based upon a Fokker-Planck equation. The viscosities are shown to depend on the particle geometry and alignment order parameters. In particular, for positive degree of alignment S-2, the calculations tend to confirm Carlsson’s conjecture relating the signs of the two viscosities to the particle geometry. Furthermore : a transition in the signs of alpha(2) for discotics and alpha(3) for nematics is predicted with increasing order parameter S-2 in accord with recent experiments. For small degree of alignment S-2, the results reproduce previous calculations obtained by Hess in a truncation approximation. The qualitative flow behaviour depends upon the signs of these viscosities.