A signicative increase in the transverse magnetoresistance and magnetothermopower in singlecrystal Bi1-x Sbx wires obtained by liquid phase casting in the temperature range 80-100 K is found. A shift to the range of lower (T < 80 K) or higher (T > 100 K) temperatures leads to the suppression of the giant increase in the magnetoresistance. The effect is interpreted in terms of the substance transition to the “gapless state”. According to the theoretical analysis of, the disappearance of the energy gap between the bands Eg is accompanied by a significant increase in mobility that leads to a sharp increase in the magnetoresistance; herein, the gapless state corresponds to the mobility maximum. While moving from the state with Eg = 0, the mobility decreases.