  The magnetic field--driven transition in the spin-Peierls system CuGeO_3
associated with the closing of the spin gap is investigated numerically. The
field dependence of the spin dynamical structure factor (seen by inelastic
neutron scattering) and of the momentum dependent static susceptibility are
calculated. In the dimerized phase (H<H_c), we suggest that the strong field
dependence of the transverse susceptibility could be experimentally seen from
the low temperature spin-echo relaxation rate 1/T_{2G} or the second moment of
the NMR spectrum. Above H_c low energy spin excitations appear at
incommensurate wave vectors where the longitudinal susceptibility chi_{zz}(q)
peaks.
