  W.Haebich (Bull. Austral. Math. Soc., 7, 1972, 279-296) presented a formula
for the Schur multiplier of a regular product of groups. In this paper first,
it is shown that the Baer-invariant of a nilpotent product of groups with
respect to the variety of nilpotent groups has a homomorphic image and in
finite case a subgroup of Haebich's type. Second a formula will be presented
for the Baer-invariant of a nilpotent product of cyclic groups with respect to
the variety of nilpotent groups.
