  We present two different versions of the consistent theory of massive
gravitons in arbitrary spacetimes which are simple enough for practical
applications. The theory is described by a non-symmetric rank-2 tensor whose
equations of motion imply six algebraic and five differential constraints
reducing the number of independent components to five. The theory reproduces
the standard description of massive gravitons in Einstein spaces. In generic
spacetimes it does not show the massless limit and always propagates five
degrees of freedom, even for the vanishing mass parameter. We illustrate these
features by an explicit calculation for a homogeneous and isotropic
cosmological background. We find that the gravitons are stable if they are
sufficiently massive, hence they may be a part of Dark Matter at present. We
discuss also other possible applications.
