Gyarmati's variational principle of thermodynamics is used to derive the equilibrium conditions as well as the equations of motion for biaxial nematic liquid crystals. From the equations of motion the nonequilibrium stress tensor is derived. The resulting equations are much easier than in the case of uniaxial nematics. This is probably a consequence of the fact that the state space can be chosen in such a way that no constraints for the generalized directors and their gradients have to be taken into account.