If, at high energies, the QCD-instanton-induced cross section reaches its unitarity limit, this process should be considered as the main source of the large transverse energy events. The events of such a type should be observed already at SppSBAR or FNAL colliders in the range of E(T) > 100-200 GeV. However, if the emission of a large number of gluons compensates no more than one half of the exponential suppression of the instanton amplitude, it will be not so easy (but at E(T) approximately 30 GeV still hopeful) to select the events induced by the QCD instantons.