Causality of massive spin-2 field in external gravity

We investigate the structure of equations of motion and lagrangian constrai nts in a general theory of massive spin-2 field interacting with external g ravity. We demonstrate how consistency with the hat limit can be achieved i n a number of specific spacetimes. One such example is an arbitrary static spacetime though equations of motion in this case may lack causal propertie s. Another example is provided by external gravity fulfilling vacuum Einste in equations with arbitrary cosmological constant. In the latter case there exists one-parameter family of theories describing causal propagation of t he correct number of degrees of freedom for the massive spin-2 field in arb itrary dimension. For a specific value of the parameter a gauge invariance with a vector parameter appears, this value is interpreted as massless limi t of the theory. Another specific value of the parameter produces gauge inv ariance with a scalar parameter and this cannot be interpreted as a consist ent massive or massless theory. (C) 2000 Elsevier Science B.V, All rights r eserved.