  We propose a new theory for the formation of rR_1 ring structures, i.e. for
ring structures with both an inner and an outer ring, the latter having the
form of ``8''. We propose that these rings are formed by material from the
stable and unstable invariant manifolds associated with the Lyapunov orbits
around the equilibrium points of a barred galaxy. We discuss the shape and
velocity structure of the rings thus formed and argue that they are in
agreement with the observed properties of rR_1 structures.
