The method of obtaining stable suspensions of heterocrystals of titanium dioxide or particles of silicon dioxide characterized by the fact that the starting material is in the form of aggregates with size more than 0.5 micrometer is mixed with an aqueous solution of pharmaceutically acceptable acid, with subsequent direction to homogenizing for the first stage of mixing, after that the obtained aqueous suspension is subjected to thermal treatment, then aqueous suspension is directed to the rotary rotor-type evaporator working under pressure lower than 100 kPa at temperature no more than 70° C. 70° C. for evaporation of pharmaceutically acceptable inorganic acid with suspension expense trough the rotor-type evaporator no more than 25 l/min and then the obtained activated particles are mixed with water in hydrodynamical cavitational homogenizer with regulated pulsating wave mode until obtaining stable suspension of heterocrystals of titanium dioxide or particles of silicon dioxide with size less than 450 nm, and presence on the lattice surface 60% up to 80% of electronically-excited triplet oxygen 3+TO23O2 in the energy centers, namely, in the quantum dots—zones of local overheating, ensuring catalytic activity for formation of active forms of oxygen in the human body of a living organism.