Current-carrying string loop dynamics in Schwarzschild-de Sitter spacetimes characterized by the cosmological parameter ?=1/3?M2 is investigated. With attention concentrated to the axisymmetric motion of string loops it is shown that the resulting motionis governed by the presence of an outer tension barrier and an inner angular momentum barrier that are influenced by the black hole gravitational field given by the mass M and the cosmic repulsion given by the cosmological constant ?. The gravitationalattraction could cause capturing of the string having low energy by the black hole or trapping in its vicinity; with high enough energy, the string can escape (scatter) to infinity.