  The unstable invariant manifolds of the short-period family of periodic
orbits around the unstable Lagrangian points $L_1$ and $L_2$ of a barred galaxy
define loci in the configuration space which take the form of a trailing spiral
pattern. In the present paper we investigate this association in the case of
the self-consistent models of Kaufmann & Contopoulos (1996) which provide an
approximation of real barred-spiral galaxies. We also examine the relation of
`response' models of barred-spiral galaxies with the theory of the invariant
manifolds. Our main results are the following: The invariant manifolds yield
the correct form of the imposed spiral pattern provided that their calculation
is done with the spiral potential term turned on. We provide a theoretical
model explaining the form of the invariant manifolds that supports the spiral
structure. The azimuthal displacement of the Lagrangian points with respect to
the bar's major axis is a crucial parameter in this modeling. When this is
taken into account, the manifolds necessarily develop in a spiral-like domain
of the configuration space, delimited from below by the boundary of a
banana-like non-permitted domain, and from above either by rotational KAM tori
or by cantori forming a stickiness zone. We construct `spiral response' models
on the basis of the theory of the invariant manifolds and examine the
connection of the latter to the `response' models (Patsis 2006) used to fit
real barred-spiral galaxies, explaining how are the manifolds related to a
number of morphological features seen in such models.
