  We investigate the steady-state solution and its bifurcations in time-delay
systems with band-limited feedback. This is a first step in a rigorous study
concerning the effects of AC-coupled components in nonlinear devices with
time-delayed feedback. We show that the steady state is globally stable for
small feedback gain and that local stability is lost, generically, through a
Hopf bifurcation for larger feedback gain. We provide simple criteria that
determine whether the Hopf bifurcation is supercritical or subcritical based on
the knowledge of the first three terms in the Taylor-expansion of the
nonlinearity. Furthermore, the presence of double-Hopf bifurcations of the
steady state is shown, which indicates possible quasiperiodic and chaotic
dynamics in these systems. As a result of this investigation, we find that
AC-coupling introduces fundamental differences to systems of Ikeda-type [Ikeda
et al., Physica D 29 (1987) 223-235] already at the level of steady-state
bifurcations, e.g. bifurcations exist in which limit cycles are created with
periods other than the fundamental ``period-2'' mode found in Ikeda-type
systems.
