  Although nuclear rings of gas and star formation are common in barred spiral
galaxies, current theories of why and how they form do not provide the level of
detail needed to quantify the effect that these rings can have on the fueling
of active galactic nuclei and on the evolution of their host galaxy. In this
paper we use detailed modeling to show that existence of nuclear rings is
directly related to the existence of the orbit family whose major axis is
perpendicular to the major axis of the bar (x_2). We explore a large range of
barred galaxy potentials and for each potential we use a two-dimensional
hydrodynamic simulation to determine whether and at what radius a nuclear ring
forms. We compare the results of the hydrodynamic simulations to numerical
integrations of periodic orbits in a barred potential and show that the rings
only form when a minimum amount of x_2 orbits exists. Because the rings migrate
inwards with time as they accumulate gas, the radius at which a nuclear ring is
seen does not give direct information on the shape of the rotation curve. We
also show that the common assumption that nuclear rings are related to an inner
Lindblad resonance is incorrect. In fact, we show that there is no RESONANCE at
the inner Lindblad resonance in barred galaxies. We also compare the
predictions of this theory to HST observations and show that it correctly
predicts the observed gas and star formation morphology of nuclear rings.
