[en] Effects are considered due to the time required for formation of ultrarelativistic positronium from a (e⁺e^-)-pair. An estimation has been performed, for the processes γ+A_Z→A_2e+A_Z and π⁰→A_2e→γ, of the thickness of the layer of material L lowering the probability of positronium formation by a factor of e as the positronium energy E_A increases. The value L increases also: for platinum L_Pt changes from 0.7 μm to 3.5 μm for E_A=6 GeV and E_A=120 GeV, respectively. The obtained values of L_Pt are 100-500 times larger than layer thickness of platinum that weakens by a factor of e the beam intensity of positronia in a stationary state: λ_Pt=7x10^-3 μm and is independent of the positronium energy. The large value of L_Pt makes possible the utilization of the photoproduction of positronium for generating beams of ultrarelativistic A_2e. The properties of atomic beams obtained with the aid of photoproduction and from the decay of π⁰-mesons are discussed. Experiments are proposed which will permit detailed investigation of the formation of positronium from a (e⁺e^-)-pair. 23 refs.; 4 figs.; 2 tabs