Cl-oss-tie shift registers, as based on nucleation and propagation of Bloch lines along domain walls in permalloy films, are of curren€ interest being 'silicon compatible , small, cheap, and non-volatile /1 to 3/. Shift rates up to 20 Mbits/s are expected. However, the actual dynamics of the devices have not been studied yet at such high frequencies.Resonance ,oscillations and relaxation of Bloch lines may interfere. They must be well understood in order to avoid malfunction of the cross-tie memories. Therefore, oscillation proper-