  We study the influence of an imperfect structure of a crystalline undulator
on the spectrum of the undulator radiation. The main attention is paid to the
undulators in which the periodic bending in the bulk appears as a result of a
regular (periodic) surface deformations. We demonstrate that this method of
preparation of a crystalline undulator inevitably leads to a variation of the
bending amplitude over the crystal thickness and to the presence of the
subharmonics with smaller bending period. Both of these features noticeably
influence the monochromatic pattern of the undulator radiation.
