  We generalize the Landau-Khalatnikov hydrodynamic theory for superfluid
helium to two-component (binary) Bose mixtures at arbitrary temperatures. In
particular, we include the spin-drag terms that correspond to viscous coupling
between the clouds. Therefore, our theory not only describes the usual
collective modes of the individual components, e.g., first and second sound,
but also results in new collective modes, where both constituents participate.
We study these modes in detail and present their dispersions using
thermodynamic quantities obtained within the Popov approximation.
