The subject of the paper is the autonomous delay monotone cyclic feedback system of the form

${\dot{x}}^{0}\left(t\right)={f}^{0}({x}^{0}\left(t\right),{x}^{1}\left(t\right))$,

${\dot{x}}^{i}\left(t\right)={f}^{i}({x}^{i-1}\left(t\right)$,

${x}^{i}\left(t\right)$,

${x}^{i+1}\left(t\right))$,

$1\le i\le N-1$,

${\dot{x}}^{N}\left(t\right)={f}^{N}({x}^{N-1}\left(t\right)$,

${x}^{N}\left(t\right)$,

${x}^{0}(t-1))$, where the functions

${f}^{0}$,

${f}^{1},\cdots ,{f}^{N}$ satisfy some monotonicity conditions with respect to their first and last arguments. The authors show that under rather mild conditions on the nonlinearities

${f}^{0}$,

${f}^{1},\cdots ,{f}^{N}$ the Poincaré-Bendixson theorem holds in force: either (a) the

$\omega $-limit set

$\omega \left(x\right)$ of a bounded solution

$x$ is a single non-constant periodic orbit; or, else, (b) all

$\alpha $- and

$\omega $-limit points of any solution in

$\omega \left(x\right)$ are equilibrium points of the system. The most part of the paper is devoted to the proof of this result. In Section 7 the authors investigate and provide very interesting results on the behavior of the periodic solutions with an emphasis on the winding number of the curve

$t\to ({x}^{i}\left(t\right),{x}^{i+1}\left(t\right))$ on the plane, while in the last section they examine the connection between oscillation of a periodic solution and its instability.