  We investigate the Landau and Baliaev damping of the collective modes in a
two-component Bose gas using the mean-field approximation. We show that due to
the two body atom-atom interaction, oscillations of each component is coupled
to the thermal excitations of the other component which gives rise to creation
or destruction of the elementary excitations that can take place in the two
separate components.In addition we find that the damping is also enhanced due
to inter-component coupling.
