[en] The amplitudes of high energy hadron interactions with light nuclei (up to ¹⁶O) in the complex momenta theory with αsub(p)sup(0) > 1 are obtained. They are valid in the attainable energy range. The numerical calculation for the differential and total cross sections of p, anti p, π-mesons and Ksup(+-)-mesons interactions with deuteron and ⁴He are made. The comparison with modern experimental data for the hadron-deuteron scatterings is made. The effects of inelastic screening were taken into account by means of the shower gain of the quazi-eikonal approximation