The hopping motion of charged light particles coupled to superconducti
ng electrons as well as to phonons is investigated within the framewor
k of a two-state model. Sufficiently far below the transition temperat
ure T(c) the hopping rate is dominated by one-phonon processes if the
static energy shifts between the particle ground states are finite but
smaller than twice the BCS energy gap. In the opposite limit of large
energy asymmetries phonon coupling does not crucially influence the j
ump rates. The role of nonlinear lattice coupling is investigated.