  The cross section for the $^3$He(e, e$'$d)p reaction has been measured as a
function of the missing momentum $p_m$ in q$\omega$ -constant kinematics at
beam energies of 370 and 576 MeV for values of the three-momentum transfer $q$
of 412, 504 and 604 \mevc. The L(+TT), T and LT structure functions have been
separated for $q$ = 412 and 504 \mevc. The data are compared to three-body
Faddeev calculations, including meson-exchange currents (MEC), and to
calculations based on a covariant diagrammatic expansion. The influence of
final-state interactions and meson-exchange currents is discussed. The
$p_m$-dependence of the data is reasonably well described by all calculations.
However, the most advanced Faddeev calculations, which employ the AV18
nucleon-nucleon interaction and include MEC, overestimate the measured cross
sections, especially the longitudinal part, and at the larger values of $q$.
The diagrammatic approach gives a fair description of the cross section, but
under(over)estimates the longitudinal (transverse) structure function.
