[en] Experimental results are presented on proton-deuteron and deuteron-deuteron elastic scattering measured at the two highest ISR energies, √s=53 GeV and √s=63 GeV. The data cover the single- and multiple-scattering regions over a wide interval of four-momentum transfer t. In both reactions clear evidence is found for a substantial t-dependent contribution of inelastic intermediate states in the multiple-scattering region, as well as in single scattering. In the analysis the Glauber multiple-scattering theory extended to include inelastic shadow effects is used. This extension of the basic theory contains as input a triple-Regge parametrization describing the high-mass inclusive spectrum. The analysis of inelastic corrections to multiple scattering on deuterons at high energies is shown to provide a sensitive test of different parametrizations of inclusive production in proton-proton collisions. (Auth.)