  We study the decay rate $\Gamma(k)$ of density excitations of two-component
Bose-Einstein condensates at zero temperature. Those excitations, where the two
components oscillate in phase, include the Goldstone mode resulting from
condensation. While within Bogoliubov approximation the density sector and the
spin (out-of-phase) sector are independent, they couple at the three-phonon
level. For a Bose-Bose mixture we find that the Belyaev decay is slightly
modified due to the coupling with the gapless spin mode. At the phase
separation point the decay rate changes instead from the standard $k^5$ to a
$k^{5/2}$ behaviour due to the parabolic nature of the spin mode. In presence
of coherent coupling between the two components the spin sector is gapped and,
away from the ferromagnetic-like phase transition point, the decay of density
mode is not affected. On the other hand at the transition point, when the spin
fluctuations become critical, the Goldstone mode is not well defined anymore
since $\Gamma(k)\propto k$. As a consequence, we show that the friction induced
by a moving impurity is enahnced -- a feature which could be experimentally
tested. Our results apply to every non-linear 2-component quantum hydrodynamic
Hamiltonian which is time-reversal invariant, and possesses an $U(1)\times
{\mathbf Z}_2$ symmetry.
