We report on unusual photoconductivity under the action of strong terahertz laser pulses in PbTe(Ga) single crystals at low temperatures. The character and even the sign on the photosignal depends on the level of photoexcitation: the photoconductivity is positive and persistent at high degrees of excitation, whereas it is negative and non-persistent at low levels of excitation. We show that this non-trivial photoelectric behaviour is due to formation of local electron states in the close vicinity of the quasi-Fermi level. These local states may be formed only when the quasi-Fermi level lies on the background of an allowed energy band with a relatively high density of states.