The production of antiprotons in pp collisions is investigated close to threshold where experimental data about the total cross section are not available. We analyze the latter reaction within the LUND string model for inclusivep production and within the framework of a one-boson exchange model for the exclusive reaction pp → pppp. The application of our new results to the analysis of subthreshold antiproton production in d + p and d + d collisions shows cross sections that are much lower than expected before. Nevertheless, the comparison of experimentalp differential cross sections from d+ p and d+ d is expected to provide valuable information about a nonnucleonic component in the deuteronwavefunction. * supported by BMBF and the Russia Foundation for the fundamental Research