The structure of accretion discs illuminated by X-rays is investigated. For high values of X-ray heating no static disc solution was found, while for low values of heating a corona was formed above the disc. This paper also deals with the structure of winds above the accretion disc. The wind parameters are the height of the critical point and the X-ray heating at that point. In contrast with previous treatments of the problem, however, we impose the condition of self-consistency between the wind and the disc structures. This condition restricts the space of possible solutions. In the high X-ray illumination case the only possible solution is the supersonic solution, implying evaporation of the disc. Only a very narrow range of X-ray heating and critical-point heights yields the proper wind solution that agrees with the disc solution. Finally, a self-consistent model of an accretion disc and a wind is presented.