  The deuteron break-up exclusive reaction $p+d \to N(180^{\circ}) +
(NN)(0^{\circ})$ is considered in the framework of the one-nucleon-exchange
mechanism at the incident proton kinetic energy 0.2--2 GeV and the relative
energy of nucleons in the forward going final NN-pair $E_{NN}=0$--20 MeV, that
is close to the kinematical conditions of the planned experiment at COSY. The
off-energy-shell effects resulting, in particular, in the node of the
half-off-shell $^1S_0$-state partial NN-scattering amplitude and the role of
higher partial waves in the subprocess $pN\to pN$ are analysed and found to be
very important, especially for the reaction $p+d \to n(180^{\circ}) +
(pp)(0^{\circ})$.
  The accuracy of some approximate relations between the cross sections of
elastic $pd$-scattering and deuteron break-up is examined in the framework of
the mechanism in question.
