  We explore a simple extension to the Standard Model containing two gauge
singlets: a Dirac fermion and a real pseudoscalar. In some regions of the
parameter space both singlets are stable without the necessity of additional
symmetries, then becoming a possible two-component dark matter model. We study
the relic abundance production via freeze-out, with the latter determined by
annihilations, conversions and semi-annihilations. Experimental constraints
from invisible Higgs decay, dark matter relic abundance and direct/indirect
detection are studied. We found three viable regions of the parameter space,
and the model is sensitive to indirect searches.
