QED processes at electron-positron colliders are considerd. We present differential cross-sections for large-angle Bhabha scattering, annihilation into muons and photons. Radiative corrections in the first order are taken into account exactly. Leading logarithmic contributions are calculated in all orders by means of the structure-function method. An accuracy of the calculation can be estimated about 0.2%.

Events with tagged photons in the process of electron-positron annihilation into hadrons are considered. The initial state radiation is suggested to scan the hadronic cross section with the energy. QED radiative corrections are taken into account. The results for the total and exclusive cross sections are given in an analytic form. Some numerical estimates are presented.

The explicit formulae for radiative correction (RC) calculation for elastic ep-scattering is presented. Two typical measurements of polarization observables such as beam-target asymmetry or recoil proton polarization, are considered. Possibilities to take into account realistic experimental acceptances are discussed. The Fortran code MASCARAD for providing the RC procedure is presented. Numerical analysis is done for kinematical conditions of TJNAF.

We study a parity-conserving single-spin beam asymmetry of elastic electron-proton scattering induced by an absorptive part of the two-photon exchange amplitude. It is demonstrated that excitation of inelastic hadronic intermediate states by the consecutive exchange of two photons leads to logarithmic and double-logarithmic enhancement due to contributions of hard collinear quasi-real photons. The asymmetry at small electron scattering angles is expressed in terms of the total photoproduction cross section on the proton, and is predicted to reach the magnitude of 20-30 parts per million. At these conditions and fixed 4-momentum transfers, the asymmetry is rising logarithmically with increasing electron beam energy, following the high-energy diffractive behavior of total photoproduction cross section on the proton.

We calculated two-photon exchange effects for elastic electron-proton scattering at high momentum transfers. The corresponding nucleon Compton amplitude is defined by two space-like virtual photons that appear to have significant virtualities. We make predictions for a) a single-spin beam asymmetry, and b) a single-spin target asymmetry or recoil proton polarization caused by an unpolarized electron beam.