We consider a macroscopic charge-current carrying (cosmic) string in the background of a Schwarzschild black hole. The string is taken to be circular and is allowed to oscillate and to propagate in the direction perpendicular to its plane (that is parallel to the equatorial plane of the black hole). Numerical investigations indicate that the system is non-integrable, but the interaction with the gravitational field of the black hole still gives rise to various qualitatively simple processes like 'adiabatic capture' and 'string transmutation'.