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The system considered in this paper consists of two equations $(k=1,2)$ $\dotx(t)=(-1)^{k-1} (0\le t<\infty),\,k(0)=1,\,x(0)=0,\,x(t)\not\in\{0,1\}(-1\let<0),$ that change mutually in every instant $t$ for which$x(t-\tau)\in\{0,1\}$, where $\tau={\rm const}>0$ is given. In this paper thebehavior of the solutions is characterized for every $\tau\in(4/3, 3/2)$, i. e.in case not covered in \cite{ADM}; as it was noted there, this behavior turnedout to be more complex then when $\tau\in(3/2,\infty)$. Thus the behavior ofthe solutions of this system with critical set $K=\{0,1\}$ is characterized forevery $\tau>0$.

On the simplest system with retarding switching and 2-point critical set.- Functional Differential Equations