  In the first part, we give a self contained introduction to the theory of
cyclic systems in n-dimensional space which can be considered as immersions
into certain Grassmannians. We show how the (metric) geometries on spaces of
constant curvature arise as subgeometries of Moebius geometry which provides a
slightly new viewpoint. In the second part we characterize Guichard nets which
are given by cyclic systems as being Moebius equivalent to 1-parameter families
of linear Weingarten surfaces. This provides a new method to study families of
parallel Weingarten surfaces in space forms. In particular, analogs of Bonnet's
theorem on parallel constant mean curvature surfaces can be easily obtained in
this setting.
