  We study properties of basic solutions in systems with dime delays and
$S^1$-symmetry. Such basic solutions are relative equilibria (CW solutions) and
relative periodic solutions (MW solutions). It follows from the previous theory
that the number of CW solutions grows generically linearly with time delay
$\tau$. Here we show, in particular, that the number of relative periodic
solutions grows generically as $\tau^2$ when delay increases. Thus, in such
systems, the relative periodic solutions are more abundant than relative
equilibria. The results are directly applicable to, e.g., Lang-Kobayashi model
for the lasers with delayed feedback. We also study stability properties of the
solutions for large delays.
