[en] The diffusion scattering of electrons and X-rays in the solid solutions of the molybdenum base alloys with rhenium (up to 40 at. %Re) has been studied. A model is proposed of the alloys structure described by means of the wave spectrum of shifts distorting the bcc lattice, which results in the formation of local atomic configurations with a structure close to the structure of the sigma-phase type. The effects observed are discussed as being common in the investigated alloys and in the alloys with bcc lattice based on Hf, Ti, Zr in which the structure can be related with the availability of the near order of shifts