[en] The explicit expressions for the differential and total cross sections of the photoproduction of the bound states /e⁺e^-/ and /μ⁺μ^-/ in the Coulomb field of a nucleus are received. The relation between an effective cross section of a generation of elementary atom, which is a bound state of two charged particles, and the effective cross section of a generation of these charged particles moving free with almost same velocities (Lorentz-factors) is used. The effect of the screening of the nucleus charge by atom electrons in the limit of very high energies is taken into account. The exact formula for the differential cross section of the positronium photoproduction in the Coulomb field of a nucleus agrees with the result of the approximate calculation by the Weizsaecker-Williams method of equivalent photons at ultrarelativistic energies and very small angles