  We investigate the behavior of the doubly heavy spin$-3/2$ baryons in cold
nuclear matter. In particular, we study the variations of the spectroscopic
parameters of the ground state $\Xi^*_{QQ'}$ and $\Omega^*_{QQ'}$ particles,
with $ Q $ and $ Q' $ being $b $ or $ c $ quark, with respect to the changes in
the density of the nuclear medium. We find the shifts on the parameters under
question at saturation medium density compared to their vacuum values. It is
observed that the parameters of the $\Xi^*_{QQ'}$ states containing two heavy
quarks and one up or down quark are affected by the medium, considerably. The
parameters of the $\Omega^*_{QQ'}$ states containing two heavy quarks and one
strange quark, however, do not show any sensitivity to the density of the cold
nuclear medium. We also discuss the variations of the vector self-energy at
each channel with respect to the changes in the density. The negative shifts in
the mass of $\Xi^*_{QQ'}$ states due to nucleons in the medium can be used to
study the doubly heavy baryons' interactions with the nucleons. The results
obtained can also be used in analyses of the results of the future in-medium
experiments.
