  Recently modified gravitational theories which mimic the behaviour of dark
matter, the so-called "Mimetic Dark Matter", have been proposed. We study the
consistency of such theories with respect to the absence of ghost instability
and propose a new tensor-vector-scalar theory of gravity, which is a
generalization of the previous models of mimetic dark matter with additional
desirable features. The original model proposed by Chamseddine and Mukhanov
[JHEP 1311 (2013) 135, arXiv:1308.5410] is concluded to describe a regular
pressureless dust, presuming that we consider only those configurations where
the energy density of the mimetic dust remains positive under time evolution.
For certain type of configurations the theory can become unstable. Both
alternative modified theories of gravity, which are based on a vector field
(tensor-vector theory) or a vector field and a scalar field
(tensor-vector-scalar theory), are free of ghost instabilities.
