The production of antiprotons in pp collisions is investigated close t
o threshold where experimental data about the total cross section are
not available. We analyze the latter reaction within the LUND string m
odel for inclusive (p) over bar production and within the framework of
a one-boson exchange model for the exclusive reaction pp --> ppp (p)
over bar. The application of our new results to the analysis of subthr
eshold antiproton production in d + p and d + d collisions shows cross
sections that are much lower than expected before. Nevertheless, the
comparison of experimental (p) over bar differential cross sections fr
om d + p and d + d is expected to provide valuable information about a
nonnucleonic component in the deuteron wavefunction.