  Starting from a dynamic tensor model about two second-order tensors, we
derive the frame hydrodynamics for the biaxial nematic phase using the Hilbert
expansion. The coefficients in the frame model are derived from those in the
tensor model. The energy dissipation of the tensor model is maintained in the
frame model. The model is reduced to the Ericksen--Leslie model if the biaxial
bulk energy minimum of the tensor model is reduced to a uniaxial one.
