  We study properties of dark matter halos in a variety of models which include
Dark Energy (DE). We consider both DE due to a scalar field self--interacting
through Ratra-Peebles or SUGRA potentials, and DE with constant negative
w=p\rho >-1. We find that at redshift zero the nonlinear power spectrum of the
dark matter, and the mass function of halos, practically do not depend on DE
state equation and are almost indistinguishable from predictions of the LCDM
model. This is consistent with the nonlinear analysis presented in the
accompanying paper. It is also a welcome feature because LCDM models fit a
large variety of data. On the other hand, at high redshifts DE models show
substantial differences from LCDM and substantial differences among themselves.
Halo profiles differ even at z=0. DE halos are denser than LCDM in their
central parts because the DE halos collapse earlier. Nevertheless, differences
between the models are not so large. For example, the density at 10 kpc of a DE
\~10^{13}Msun halo deviates from LCDM by not more than 50%. This, however,
means that DE is not a way to ease the problem with cuspy dark matter profiles.
Addressing another cosmological problem - abundance of subhalos -- we find that
the number of satellites of halos in various DE models does not change relative
to the LCDM, when normalized to the same circular velocity of the parent halo.
To summarize, the best way to find which DE model fits the observed Universe is
to look for evolution of halo properties. For example, the abundance of galaxy
groups with mass larger than 10^{13}\Msun at z> 2 can be used to discriminate
between the models, and, thus, to constrain the nature of DE.
