  We report on our work on the SU(2)_L x SU(2)_R symmetric Higgs Yukawa Model
with mirror fermion action. Our model describes a fermion Higgs system in the
limit of vanishing gauge coupling. Setting the bare Yukawa coupling of the
mirror fermions G_\chi to zero, we want to determine the triviality bounds on
the renormalized Yukawa coupling of the fermions G_{R\psi} and the scalar
self-coupling g_R on 8^3x16 and 16^3x32 lattices.
