  We consider the two-component delay system $\varepsilon
x^{\prime}(t)=-x(t)-y(t)+f(x(t-1)),$ $y^{\prime}(t)=\eta x(t)$ with small
parameters $\varepsilon,\eta$, and positive feedback function $f$. Previously,
such systems have been reported to model switching in optoelectronic
experiments, where each switching induces another one after approximately one
delay time, related to one round trip of the signal. In this paper, we study
these delay-induced switched states. We provide conditions for their existence
and show how the formal limits $\varepsilon\to0$ and/or $\eta\to0$ facilitate
our understanding of this phenomenon.
