In the paper [Large-amplitude periodic solutions for differential equations with delayed monotone positive feedback, JDDE 23 (2011), no. 4, 727–790], we have constructed large-amplitude periodic orbits for an equation with delayed monotone positive feedback. We have shown that the unstable sets of the large-amplitude periodic orbits constitute the global attractor besides spindle-like structures. In this paper we focus on a large-amplitude periodic orbit $${\mathcal {O}}_{p}$$ O p with two Floquet multipliers outside the unit circle, and we intend to characterize the geometric structure of its unstable set $${\mathcal {W}}^{u}\left( {\mathcal {O}}_{p}\right) $$ W u O p . We prove that $${\mathcal {W}}^{u}\left( {\mathcal {O}}_{p}\right) $$ W u O p is a three-dimensional $$C^{1}$$ C 1 -submanifold of the phase space and admits a smooth global graph representation. Within $${\mathcal {W}}^{u}\left( {\mathcal {O}}_{p}\right) $$ W u O p , there exist heteroclinic connections from $${\mathcal {O}}_{p}$$ O p to three different periodic orbits. These connecting sets are two-dimensional $$C^{1}$$ C 1 -submanifolds of $${\mathcal {W}}^{u}\left( {\mathcal {O}}_{p}\right) $$ W u O p and homeomorphic to the two-dimensional open annulus. They form $$C^{1}$$ C 1 -smooth separatrices in the sense that they divide the points of $${\mathcal {W}}^{u}\left( {\mathcal {O}}_{p}\right) $$ W u O p into three subsets according to their $$\omega $$ ω -limit sets.