The phenomena of low-field hysteresis of the magnetoimpedance (MI) in zero-magnetostrictive amorphous wires are studied theoretically and experimentally. We developed a mathematical model for magnetization reversal and impedance field dependence. The presented model considers the low-field hysteresis and the effect of circular bias magnetic field. It is demonstrated that the hysteresis originates from a nonzero angle $\ensuremath{\alpha}$ between the anisotropy easy axis and transversal plane. The bias field, which is produced by current running through the wire, considerably affects the MI dependence making it anhysteretic and highly asymmetric. The validity of the model is confirmed by the experiments. The main characteristics of the studied amorphous wire such as anisotropy field ${H}_{A}$, angle between the anisotropy easy axis with the transversal direction $\ensuremath{\alpha}$, and Gilbert damping constant ${\ensuremath{\alpha}}_{G}$ were obtained from the experiment in accordance with the presented model.