Using the Hall effect measurements, it is established that the sign of carriers in the LuxMn1–xS solid solutions changes upon temperature and concentration variations. The extrema in the temperature dependence of the electrical resistance and hysteresis of the electric polarization are found. The change in the sign of the exchange coupling between the nearest neighbors under electron doping is established. The magnetoresistance in the paramagnetic region is caused by the change in the induced electric polarization in a magnetic field. In the LuxMn1−xS compound, the magnetoresistance changes sign from negative to positive at the heating. The resistance decreases in a magnetic field due to a change in the induced electric polarization of clusters with lutetium in a magnetic field. The positive magnetoresistance at high temperatures is explained within the Maxwell–Wagner model with two conduction channels.