  The flux of cosmic ray antiprotons from neutralino annihilations in the
galactic halo is computed for a large sample of models in the MSSM (the Minimal
Supersymmetric extension of the Standard Model). We also revisit the problem of
estimating the background of low-energy cosmic ray induced secondary
antiprotons, taking into account their subsequent interactions (and energy
loss) and the presence of nuclei in the interstellar matter.
  We consider a two-zone diffusion model, with and without a galactic wind. We
find that, given the uncertainties in the background predictions, there is no
need for a primary (exotic) component to explain present data. However,
allowing for a signal by playing with the uncertainties in the background
estimate, we discuss the characteristic features of the supersymmetric models
which give a satisfactory description of the data. We point out that in some
cases the optimal kinetic energy to search for a signal from supersymmetric
dark matter is above several GeV, rather than the traditional sub-GeV region.
  The large astrophysical uncertainties involved do not, one the other hand,
allow the exclusion of any of the MSSM models we consider, on the basis of
data.
  We present besides numerical results also convenient parameterizations of the
antiproton yields of all `basic' two-body final states. We also give examples
of the yield and differential energy spectrum for a set of supersymmetric
models with high rates.
  We also remark that it is difficult to put a limit on the antiproton lifetime
from present measurements, since the injection of antiprotons from neutralino
annihilation can compensate the loss from decay.
