  An electron passing through a counter propagating intense laser beam can
interact with a few laser photons with emission of a hard photon in each
collision event. In contrast with the well-known nonlinear Compton
backscattering process the above mentioned process may be named as multiple
Compton backscattering process (MCBS). In this paper we have investigated the
evolution of the electron energy distribution during MCBS process using
Monte-Carlo (M-C) simulation. The main characteristics of such a distribution
as mean energy and variance obtained by M-C technique were compared with
analytical solutions of kinetic equations. We found the kinematic region where
the analytical solutions are applicable with a good accuracy. A photon
spectrum, even for the case when each electron emits one photon (in average)
differs significantly from that described by the Klein-Nishina formula.
