The equations governing the flow behavior of the biaxial nematic phase are derived and presented in such a form that it is easily seen that the fluid dynamic theory of biaxial nematics can be formulated as a natural generalization of the Leslie-Ericksen theory of uniaxial nematics. It is shown that in order to describe the flow behaviour of biaxial nematics, fifteen viscosity coefficients, related by three Onsager relations, are required. With the biaxial nematic stress tensor as a starting point we discuss the concept of viscous torques, and show how a good qualitative understanding of the flow behaviour of the system follows by studying them. We show that three rotational viscosities and nine effective shearing viscosities have to be defined in order to characterize the viscous behaviour of biaxial nematics completely. Thus it is possible to design sufficient experiments to measure the twelve independent viscosity coefficients included in the theory. We also derive the possible equilibrium orientations for a biaxial nematic when subjected to shear flow, and give a brief discussion of their stability.