The low-temperature conductivity of antiferromagnetic cuprates La _2-xSr_xCuO₄, prepared by solid-phase synthesis was investigated. The concentration of stron-tium in the samples was 0.01, 0.005 and 0.001. In the temperature range T < 100 K for all the samples the conduction mechanism was appropriate to variable range hopping for 3D systems. For T > T_N (where T_N is the Neel temperature) the transition to a metallic type of conductivity was observed. We have found nonlinear effects in low-temperature conductivity, magnetoresistivity and current-driven negative differ-ential resistivity. We also found out that nonlinear be-havior of conductivity increased with decreasing strontium concentration. For temperatures T < 10 K, the effect of positive magnetoresistance was observed. We suggest that this effect can be attributed to the pre-sence of a new low-temperature magnetic phase (spin density wave).