Using the four-spacecraft Cluster system, we analyze rapid neutral sheet crossings near the Cluster apogee at about -18RE. In case studies of multiple oscillations of the locally quiet plasma sheet as well as in a statistical study of oscillations in dawn and dusk near-flank plasma sheet portions we typically obtain that locally these dynamical current sheets are very corrugated and that subsequent crossings basically show portions of large-scale kink-like waves propagating from the tail center toward flanks. Propagation velocities are in the range of several tens km/s for the locally quiet sheets, and up to 200 km/s during fast flows. These results suggest that the flapping motions are of internal origin and that kink-like waves are emitted in the central part of the tail by some impulsive source and propagate toward the tail flanks. The wave properties do not match any local excitation mechanism previously discussed so far in the literature.