[en] The production of cumulative nuclei of ²H in ¹⁶O_p collisions at a momentum of 3.25 GeV/c per nucleon was studied for the first time under conditions of a 4π acceptance. The parameter T₀ characterizing the slope of the spectrum of invariant cross sections for cumulative-deuteron production in ¹⁶Op interactions was determined. The contribution to cumulative-deuteron production from the decay of the alpha-particle clusters in nuclei upon slow-pion absorption by these clusters was found on the basis of an analysis of the momentum distribution of these cumulative nuclei. The estimates obtained for the contribution of these processes from a comparison of the mean multiplicities of particles and fragments in cumulative and noncumulative events agree well with the respective result extracted from the momentum distribution of cumulative deuterons.