  Two scenarios for the penetration of relativistically intense laser radiation
into an overdense plasma, accessible by self-induced transparency, are
presented. For supercritical densities less than 1.5 times the critical one,
penetration of laser energy occurs by soliton-like structures moving into the
plasma. At higher background densities laser light penetrates over a finite
length only, that increases with the incident intensity. In this regime
plasma-field structures represent alternating electron layers separated by
about half a wavelength by depleted regions.
