We consider a simple model for the Universe reheating, which consists
of a single self-interacting scalar field in Minkowskian space-time. M
aking use of the existence of an additional small parameter proportion
al to the amplitude of the initial spatially homogeneous field oscilla
tions, we show that the behavior of the field dan be found reliably. W
e describe the evolution of the system from the homogeneous oscillatio
ns to the moment when thermalization is completed. We argue that some
properties found for this model may be the common features of realisti
c theories.