  In this paper, based on the Hirota and Maxwell-Bloch (H-MB) system and its
application in the theory of the femtosecond pulse propagation through an
erbium doped fiber, we define two kinds of nonlocal Hirota and Maxwell-Bloch
(NH-MB) systems, namely, $PT$-symmetric NH-MB system and reverse space-time
NH-MB system. Then we construct the Darboux transformations of these NH-MB
systems. Meanwhile, we derive the explicit solutions by the Darboux
transformations.
