Measurements of peak shifts in the derivative of magnetisation with time versus driving field are performed on Co74Fe6B20 amorphous ribbons, carrying an electrical current. Ribbons with a cross‐section of 2 × 0.025 mm2 are produced by melt‐spinning. Magnetic anisotropy is induced in them prior to the measurements, by annealing at 300 °C in a non‐saturated state. Measurements of the peak shift give information on the degree of stabilisation of domain walls with depth in the ribbons. For short annealing times (≈︁1 min), the stabilisation is inhomogeneous through the thickness; for long annealing times (≈︁2 h), just a slight inhomogeneity is obtained. From these results it is deduced that relaxation frequencies are highest, but not the same, in the vicinity of the free and the contact ribbon surfaces. It is also shown that inhomogeneous stabilisation of domain walls is induced in samples upon their production.