The paper deals with the investigation of polymerization processes in acryl compositions which were developed first for stereolithography using a promising photo-initiating laser emission of a visible range. The processes of oxidizing polymerization of a photo-polymerizing composition at very low concentrations of an antioxidant [X] and a concentration of dissolved oxygen [O2] > 10-7 ÷ 10-8 mole/l are considered. It is shown that the appearance of an induction period is typical just of reactions passing in a closed system, and in an open one a reaction passes without an induction period. Under these conditions the reaction products are poly-peroxides of a low-molecular structure. There are also considered the processes of polymerization at the dissolved oxygen concentration [O2] > 10-7 ÷ 10-8 mole/l and at high concentrations of anti-oxidant X. It is determined that after a lapse of time when an oxidant is spent a velocity of oxygen expense increases as a result of which in the layers more remote from the boundary of phase division the composition – air the open system transforms into a closed one. In these layers the rate of oxygen diffusion appeared to be less of the rate of its expense in reactions of monomer oxidation. The investigation results explain the mechanism of a track formation at the irradiation of a photo-polymerizing composition with a laser beam.