  We study heat conduction in one dimensional lattice dynamical systems far
from equilibrium. The Fermi-Pasta-Ulam model and the $\phi^4$ model are
numerically compared to elucidate differences between momentum-conserving and
nonconserving systems. As a results, it is found that the heat flux in the
$\phi^4$ model does not increase monotonically as the temperature differences
at the ends of the lattice is increased, while it does in the FPU chain.
