  A method to derive the convenient representations for many two-photon
amplitudes is suggested. It is based on the use of the gauge in which the
photon propagator has only space components. The amplitudes obtained have no
any strong numerical cancellations and, therefore, are very convenient for
numerical evaluations. Our approach is illustrated by the consideration of the
processes $e^+e^-\to e^+e^-e^+e^-$, $e^+e^-\rightarrow e^+e^-\mu^+\mu^-$, and
$e^+e^-\to \mu^+\mu^-\pi^+\pi^-$. The method is extended on the case of
polarized particles. The amplitudes obtained in this approach have been
employed for extension of the event generator developed by F.A. Berends, P.H.
Daverveldt, and R. Kleiss.
