  We study the small--angle double bremsstrahlung in $e^-e^\pm$ scattering for
a jet kinematics where both photons move along the electron direction. This
region gives the main contribution to the cross section. We present analytic
expressions for all 64 amplitudes with arbitrary helicity states of the initial
and final leptons and the produced photons convenient for analytic and
numerical studies. The accuracy of the obtained amplitudes is given omitting
only terms of the order of m^2/E_j^2, \theta_j^2 and \theta_j m/E_j. The
helicity amplitudes for the cross channel \gamma e^\pm \to \gamma e^+e^- +
e^\pm are given. Several limits for the helicity amplitudes of hard or soft
final particles are considered.

High Energy Physics - Phenomenology