We report the results of experiments in which positronium (Ps) atoms, optically excited to Rydberg-Stark states with principal quantum numbers ranging from
n
=
13
to 19, were transported along the axis of a multiring electrode structure. By applying alternate positive and negative potentials to the ring electrodes, inhomogeneous electric fields suitable for guiding low-field-seeking atoms along the guide axis were generated. The multiring configuration used has the advantage that once the atoms are confined within it appropriate time-varying fields can be generated for deceleration and trapping. However, in this type of structure the possibility of nonadiabatic transitions of the fast (100 km/s) Ps atoms to unconfined high-field-seeking states exists. We show that for typical guiding fields this is not a significant loss mechanism and that efficient Ps transport can be achieved. Our data are in accordance with a Landau-Zener analysis of adiabatic transport through the field minima and Monte Carlo simulations that take into account Ps velocity distributions, electric dipole moments, and lifetimes, as well as the electric-field distributions in the guide