The optical guiding of x-ray radiation by capillary waveguides is analysed by using the Fresnel-Kirchhoff diffraction theory and the method of images. The guiding of the continuous, short-pulse, coherent, partially coherent and incoherent waves is presented as the diffraction and interference of several x-ray beams produced in free space by the Fresnel source of the waveguide. Using the Fresnel source properties, the necessary conditions for influence of the diffraction and interference on the output characteristics of the capillary x-ray optics in the near-and far-field diffraction zones are derived. The experimental data and computer simulations presented confirm the wave optics behaviour of x-rays under such conditions.