The photorefractive properties of semi-insulating AlGaAs-GaAs multiple quantum wells are described for the transverse Franz-Keldysh geometry with the electric field in the plane of the quantum wells. Combining the strong electroabsorption of quantum-confined excitons with the high resistivity of semi-insulating quantum wells yields large nonlinear optical sensitivities. The photorefractive quantum wells have effective nonlinear optical sensitivities of n2 103 cm 2 /W and a2/ao =: 10 4 cm 2 /W for applied fields of 10 kV/cm. Photorefractive gains approaching 1000 cm-' have been observed in two-wave mixing under dc electric fields and stationary fringes. The transverse Franz-Keldysh geometry retains the general transport properties and behavior of conventional bulk photorefractive materials. The resonant excitation of free electrons and holes in the quantum wells leads to novel behavior associated with electron-hole competition. We demonstrate that under resonant excitation of electrons and holes the device resolution is fundamentally limited by diffusion lengths but is insensitive to long drift lengths.