The hysteretic behavioral features of magnetization and resistance upon remagnetization under quasistatic (up to 9 T) and pulse (up to 14 T) magnetic fields have been investigated. The relaxation processes of magnetization and resistance after the effect of 9 T magnetic field have also been studied. The mechanism of remagnetization of the antiferromagnetic insulating-ferromagnetic metallic (AFM/I–FM/M) phases and the existence of high conductivity state of the sample after removal of the magnetizing field is proposed for low temperatures. The mechanism is caused by structural transition, which is induced by magnetic field (due to magnetostriction), and slow relaxation of the FM-phase (greater volume) to the equilibrium AFM-phase (smaller volume) after the field removal. Remagnetization of Nd₀.₅Sr₀.₅MnO₃ single crystal under pulse field at low temperatures (18 K) has shown that time of the AFM/I→FM/M phase transition was lower than time of the return FM/M→AFM/I phase transition by 6 orders of magnitude.