The center of a unital near-ring module
R
M
{}_RM
is defined, leading to the construction of a lower central series and a definition of
R
R
-nilpotence. Likewise a suitable definition of commutators yields a derived series and
R
R
-solvability. When
(
R
,
+
)
(R, + )
is generated by elements which distribute over
M
M
the
R
R
-nilpotence (
R
R
-solvability) is shown to coincide with the nilpotence (solvability) of the underlying group. In this case, nilpotence has implications for
R
R
-normalizers and the Frattini submodule.