[en] The use of thin (< 10⁻³ radiation length) internal targets in cyclic accelerators leads to multiple passes (recycling effect) of electrons through them. The multiplicity of electron passes (M) is determined by the electron energy, accelerator parameters, the thickness, structure and material of a target and leads to an increase in the effective target thickness and the efficiency of radiation generation. The increase of M leads to the increase in the emittance of electron beams which can change the characteristics of radiation processes. The experimental results obtained using the Tomsk synchrotron and betatron showed the possibility of increasing the yield and brightness of coherent X-rays generated by the electrons passing (recycling) through thin crystals and periodic multilayers placed into the chambers of accelerators, when the recycling effect did not influence on the spectral and angular characteristics of generated X-rays.