  We study heat conduction in one dimensional mass disordered harmonic and
anharmonic lattices. It is found that the thermal conductivity $\kappa$ of the
disordered anharmonic lattice is finite at low temperature, whereas it diverges
as $\kappa \sim N^{0.43}$ at high temperature. Moreover, we demonstrate that a
unique nonequilibrium stationary state in the disordered harmonic lattice does
not exist at all.
