We have calculated the viscosities of a biaxial nematic liquid crystal phase of a variant of the Gay-Berne fluid [J. G. Gay and B. J. Berne, J. Chem. Phys. 74, 3316 (1981)] by performing molecular dynamics simulations. The equations of motion have been augmented by a director constraint torque that fixes the orientation of the directors. This makes it possible to fix them at different angles relative to the stream lines in shear flow simulations. In equilibrium simulations the constraints generate a new ensemble. One finds that the Green-Kubo relations for the viscosities become linear combinations of time correlation function integrals in this ensemble whereas they are complicated rational functions in the conventional canonical ensemble. We have evaluated these Green-Kubo relations for all the shear viscosities and all the twist viscosities. We have also calculated the alignment angles, which are functions of the viscosity coefficients. We find that then are three real alignment angles but a linear stability analysis shows that only one of them corresponds to a stable director orientation. The Green-Kubo results have been cross checked by nonequilibrium shear flow simulations. The results from the different methods agree very well. Finally, we have evaluated the Miesowicz viscosities [D. Baalss, Z. Naturforsch. Tell A 45, 7 (1990)]. They vary by mon than 2 orders of magnitude. The viscosity is consequently highly orientation dependent. (C) 1997 American Institute of Physics.