  A covariant formalism for physical perturbations propagating along a string
in an arbitrary curved spacetime is developed. In the case of a stationary
string in a static background the propagation of the perturbations is described
by a wave-equation with a potential consisting of 2 terms: The first term
describing the time-dilation and the second is connected with the curvature of
space. As applications of the developed approach the propagation of
perturbations along a stationary string in Rindler, de Sitter, Schwarzschild
and Reissner-Nordstrom spacetimes are investigated.
