  We discuss the problem of consistent description of higher spin massive
fields coupled to external gravity. As an example we consider massive field of
spin 2 in arbitrary gravitational field. Consistency requires the theory to
have the same number of degrees of freedom as in flat spacetime and to describe
causal propagation. By careful analysis of lagrangian structure of the theory
and its constraints we show that there exist at least two possibilities of
achieving consistency. The first possibility is provided by a lagrangian on
specific manifolds such as static or Einstein spacetimes. The second
possibility is realized in arbitrary curved spacetime by a lagrangian
representing an infinite series in curvature. In the framework of string theory
we derive equations of motion for background massive spin 2 field coupled to
gravity from the requirement of quantum Weyl invariance. These equations appear
to be a particular case of the general consistent equations obtained from the
field theory point of view.
