  The first author, in 2001, presented a structure for the Baer-invariant of a
nilpotent product of cyclic groups with respect to the variety of nilpotent
groups. In this paper, using the above structure, we prove the existence of an
${\cal N}_c$-covering group for a nilpotent product of a family of cyclic
groups. We also present a structure for the ${\cal N}_c$-covering group.
