Abstract: The propagation of multiple incoherent beams in biased two-photon non-photovoltaic photorefractive crystal is investigated under steady-state conditions. It shows that the two-photon incoherently-coupled bright-dark hybrid screening soliton families exist in the biased two-photon non-photovoltaic photorefractive crystals, and that the soliton families are formed by the mutually incoherent beams which have same polarization and wavelength. Moreover, two-photon photorefractive crystals, whose optical axis direction is same to the direction of the external field, can support bright-dark soliton families in which the peak intensity of the bright component is slightly larger than that of the dark component. When the direction of the applied electric field is reversed to that of the optical axis, the two-photon photorefractive crystals can support the bright-dark soliton families in which the peak intensity of the bright component is slightly lower than that of dark component.