We investigate the singularly perturbed monotone systems with respect to cones of rank
2
2
and obtain the so called Generic Poincaré-Bendixson theorem for such perturbed systems, that is, for a bounded positively invariant set, there exists an open and dense subset
P
\mathcal {P}
such that for each
z
∈
P
z\in \mathcal {P}
, the
ω
\omega
-limit set
ω
(
z
)
\omega (z)
that contains no equilibrium points is a closed orbit.