We consider the system of second order differential equations
\[
u
+
∇
G
(
u
)
=
e
(
t
)
≡
e
(
t
+
T
)
,
u + \nabla G(u) = e(t) \equiv e(t + T),
\]
, where the potential
G
:
R
n
→
R
G:{\mathbb {R}^n} \to \mathbb {R}
is not necessarily convex. Using critical point theory, we give conditions under which the system has infinitely many subharmonic solutions.