[en] For steels of different grades (the 20, 45Kh, OKHN3MFA steels) by the method of highest harmonics studied are the processes of remagnetization of upper layers of ferromagnetic samples of the open configuration at quasi-static measuring of external magnetic field. It is shown that the phenomenon of ''anomalous magnetization'' observed earlier only at quick decrease of external magnetic field occurs at quasi-static remagnetization as well, and the upper layers of sample achieve demagnetization state before than the deep ones. On the basis of the found phenomenon developed is a new method of nondestructive testing of heat treatment quality, and of surface hardening of ferromagnetic articles