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The magnetoimpedance effect and changes of the relaxation frequency fx are studied in CoFeSiB and CoFeMoSiB amorphous and FeCuNbSiB nanocrystalline ribbons. The evolution of the magnetostriction constant λs and relaxation frequency is analysed for the states with different magnetic anisotropies induced in the same ribbons.A monotonic decrease of the relaxation frequency is observed for shifting of λs towards positive values.