  We investigate critical masses of and circular geodesics around
doubly-degenerate stars (DDSs) which are composed of cold nuclear matter as
well as cold Fermionic dark matter (DM). We here consider asymmetric dark
Fermion with self-interaction as a DM candidate. These stars have core-envelope
structures and are categorized into baryon-enveloped and DM-enveloped,
according to the composition of their envelope. It is seen that the
baryon-enveloped and DM-enveloped classes have their own critical masses
determined mainly by the dominant component in their envelope. For a typical
parameter sets, we see that a balanced mixture of two species may lead to
smaller masses than if the either of the species is dominant.
  We also show that for a highly DM-enveloped case circular orbits in the
vacuum region terminates at the innermost stable circular orbit (ISCO) in
vacuum, but circular orbits of smaller radius are possible in the DM-envelope
forming a gap between the ISCO and the inner orbits.
