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−→e+e−e+e−, e+e−→e+e−μ+μ−, and e+e−→μ+μ−π+π−. 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. It allows for simulation of e+e−→4l and e+e−→2l2π processes with π+π− pair in the 1−− state with accounting for contributions of narrow vector resonances and ISR corrections. The calculations with arbitrary polarization of initial particles is also foreseen.