Suppose that
(
θ
,
φ
)
(\theta ,\varphi )
is a monotone (order-preserving) random dynamical system (RDS for short) with state space
V
V
, where
V
V
is a real separable Banach space with a normal solid minihedral cone
V
+
V_{+}
. It is proved that the unique equilibrium of
(
θ
,
φ
)
(\theta ,\varphi )
is globally attractive if every pull-back trajectory has compact closure in
V
V
.