  Systems with time delay play an important role in modeling of many physical
and biological processes. In this paper we describe generic properties of
systems with time delay, which are related to the appearance and stability of
periodic solutions. In particular, we show that delay systems generically have
families of periodic solutions, which are reappearing for infinitely many delay
times. As delay increases, the solution families overlap leading to increasing
coexistence of multiple stable as well as unstable solutions. We also consider
stability issue of periodic solutions with large delay by explaining asymptotic
properties of the spectrum of characteristic multipliers. We show that the
spectrum of multipliers can be splitted into two parts: pseudo-continuous and
strongly unstable. The pseudo-continuous part of the spectrum mediates
destabilization of periodic solutions.
