The dc conductivity of dye-doped nematic liquid crystal cells exhibits a characteristic transition from a cubic current-voltage relationship at applied voltages smaller than about 1 V to a linear one at voltages larger than about 1.5 V. The photoconductivity, and the related photorefractive response of these cells exhibit an apparent threshold at about the same characteristic voltage: An applied voltage larger than about 1.5 V is needed to measure sizeable photocurrents and photorefractive responses. We propose a model that is consistent with all these observations. At low applied voltages, a residual space charge limits the dc current, and prevents the participation of photoexcited charge carriers to photoconductivity and photorefractivity, while at higher applied voltages, the disappearance of the residual space charge allows the manifestation of these photoinduced responses. Experimental results seem to confirm the validity of the model. (C) 2002 American Institute of Physics.