Single phase ceramics of composition Sr(Ti1-xMgx)O3-x: 0x0.01 were prepared by sol-gel synthesis and characterized by X-ray diffraction, scanning electron microscopy, impedance spectroscopy, and current-voltage measurements. The bulk and grain-boundary conductivities increase on application of a small dc bias voltage in the range 3-200V/cm and at temperatures in the range 150 degrees C-800 degrees C. A qualitatively similar increase in conductivity occurs on increasingPO2 in the surrounding atmosphere, which shows that conduction is p type. The conductivity increase is reversible on removal of the dc bias or on reducing PO2 and is not observed in undoped SrTiO3. It is an intrinsic property of the bulk material, differs from the voltage-dependent effects observed with varistors and is attributed to changes in redox equilibria between oxygen species at the surface which cause changes in carrier concentration in the interior. A capacitive model of this low-field dc bias effect is presented and compared with a memristive model of high field resistance degradation.