The fermion-fermion stars, i.e., the dark matter self-gravitating systems m
ade from two kinds of fermions with different masses, are considered. We re
view the stability of the systems, present a comparison between the maxima
of gravitational redshift for fermion stars, compact stars, Bondi stars, bo
nson stars and fermion-fermion stars, and then investigate rotation curves
of fermion-fermion stars (two-component concentric spheres) which might be
polytropic dark matter halos of galaxies. Results show that the fermion-fer
mion stars would give rotation curves with hat part at large radii. This pr
esents a striking contrast with the rotation curve of a single component fe
rmion star which has no flat parts.