We study the properties of heat conduction in chains of coupled particles s
ubjected to different anharmonic on-site potentials. Particular emphasis is
placed on the role of breathers in saturation of the thermal conductivity
for chains with hard anharmonicity; When the chain particles are subject to
on-site potentials with soft anharmonicity, we find a characteristic tempe
rature, below which the conductivity decreases but while above which it inc
reases. [S1063-651X(99)05912-7].