摘要： A resonant laser-assisted process of the electron-positron pairs annihilation and production is studied theoretically. The second order in fine structure constant process in the laser field transforms into two consistent processes of first order in the fine structure constant: laser-assisted annihilation of initial electron-positron pair into intermediate photon and laser-assisted production of final electron-positron pair by intermediate photon under resonant conditions when virtual photon becomes real. It is demonstrated that the resonant conditions for initial pair include the excess of certain combination of the electron and positron energies over threshold energy and narrow angle between momenta of electron and positron. The same holds true for the final pair. Also, final positron emission angle can vary from zero to some maximum value. It is shown that energies of the final particles depend on this angle and can take from one to two values. A resonant differential cross section of the studied process is obtained. It is shown that the resonant differential cross section can significantly exceed the corresponding cross section without an external field (Bhabha cross section). The project calculations may be experimentally verified by the scientific facilities of pulsed laser radiation (SLAC, FAIR, XFEL, ELI, XCELS).