The magnetic properties of magnetically soft materials depend on the structural state, the domain structure, and the stabilization of the domain boundaries. By changing the structure of ferromagnetic materials, their magnetic properties may be controlled. Alloy structure may be changed by heat treatment, thermomagnetic treatment, and mechanical thermomagnetic treatment. The structure of amorphous and nanocrystalline alloys (for example, after thermomagnetic treatment) may be characterized by the presence of internal elastic distortion, the appearance of precursors to precipitation (concentration stratification of the amorphous matrix), the size of the nanograins, and the chemical composition of the nanophases. Transmission electron microscopy is widely used in investigating the structure of amorphous and nanocrystalline alloys. Additional information regarding the structure of polycrystalline alloys may be obtained by means of the Barkhausen effect [1, 2]. In the present work, we study the influence of the structure formed in thermal and thermomagnetic treatment in amorphous and nanocrystalline alloys of iron and cobalt on the Barkhausen-effect parameters. Amorphous strip (thickness 20‐25 μ m; width 5 mm) is obtained by quenching melt on a rotating copper disk. The amorphous alloy samples with different magnetostriction λ s take the form of strips and toroids. We investigate the following samples Fe 60 Co 20 Si 5 B 15 ( λ s ≈ 30 × 10 ‐6 ), Fe 5 Co 70 Si 15 B 10 ( λ s ≈ 0.5 × 10 ‐6 ), Fe 73.5 ‐ x Co x Cu 1 Nb 3 Si 13.5 B 9 ( x = 0, 10, 20, 30 at %), Fe 73.5 Cu 1 Nb 1.5 Mo 1.5 Si 13.5 B 9 , Fe 69 Cu 1 Nb 1.5 Mo 1.5 Si 13.5 B 9 Co 4.5 ( λ s ≈ 0.2 × 10 ‐6 ), and Co 81.5 Mn 9.5 Zr 9 ( λ s ∼ 0). The samples are annealed in vacuum at 300‐350 ° C to remove the quenching stress. After annealing, the samples undergo thermomagnetic treatment in a longitudinal magnetic field at various frequencies f : a constant field ( f = 0), an alternating field ( f = 50 Hz), and a highfrequency field ( f = 80 Hz) [3, 4]. Some samples undergo complex thermomagnetic treatment: annealing in a specified temperature range with the simultaneous application of constant and high-frequency magnetic fields. Some of the samples are quenched in water from the Curie temperature, in an alternating magnetic field (at 5000 ° C/min). The structure of the amorphous strip is investigated by transmission electron microscopy on a JEM-200KX microscope. Foil is prepared from alloy strip by electrolytic polishing, for electron-microscopic inspection; the thickness of the thinnest regions of the foil is 200‐300 nm. The Barkhausen-effect parameter considered is the emf e of the flux of Barkhausen discontinuities, which is averaged over the remagnetization period. The flux of Barkhausen discontinuities is observed visually on the oscillograph screen. The emf is measured on the strip samples by means of an applied sensor; the static hysteresis loops are determined. On toroidal samples, the static hysteresis loop, initial magnetic permeability μ 0 , and magnetic losses P 0.2/20000 are determined. The magnetic losses are calculated at frequency 20 kHz and induction 0.2 T, from the area of the dynamic hysteresis loops recorded stroboscopically. The initial magnetic permeability is determined at 80 Hz in a 0.05-A/m field. The basic characteristics (Curie point T C and solidification temperature T so ) of amorphous alloys, nanocrystals, and nanocrystalline structures (denoted by one, two, and three asterisks, respectively) are as follows: