  The article describes Boltzmann equations for a potential case of
multi-particle dark matter with symmetric and asymmetric dark matter components
in a model-independent approach. We focus on the specific scenario where one of
the DM candidates remains completely invisible, having only hidden sector
interactions with the other dark matter constituent referred to as ``dark
annihilation". The possible effect of non-standard expansion of the universe on
the dark matter abundance is also taken into account.
