  We study the stability of a recently proposed model of scalar-field matter
called mimetic dark matter or imperfect dark matter. It has been known that
mimetic matter with higher derivative terms suffers from gradient instabilities
in scalar perturbations. To seek for an instability-free extension of imperfect
dark matter, we develop an effective theory of cosmological perturbations
subject to the constraint on the scalar field's kinetic term. This is done by
using the unifying framework of general scalar-tensor theories based on the ADM
formalism. We demonstrate that it is indeed possible to construct a model of
imperfect dark matter which is free from ghost and gradient instabilities. As a
side remark, we also show that mimetic $F({\cal R})$ theory is plagued with the
Ostrogradsky instability.
