  We study the impact of semi-annihilations x_i x_j <-> x_k X, where x_i is any
dark matter and X is any standard model particle, on dark matter phenomenology.
We formulate minimal scalar dark matter models with an extra doublet and a
complex singlet that predict non-trivial dark matter phenomenology with
semi-annihilation processes for different discrete Abelian symmetries Z_N, N>2.
We implement two such example models with Z_3 and Z_4 symmetry in micrOMEGAs
and work out their phenomenology. We show that both semi-annihilations and
annihilations involving only particles from two different dark matter sectors
significantly modify the dark matter relic abundance in this type of models. We
also study the possibility of dark matter direct detection in XENON100 in those
models.
