  We model the influence of an in-plane magnetic field on the orbital motion of
electrons in rhombohedral graphene multilayers. For zero field, the low-energy
band structure includes a pair of flat bands near zero energy which are
localized on the surface layers of a finite thin film. For finite field, we
find that the zero-energy bands persist and that level bifurcations occur at
energies determined by the component of the in-plane wave vector $q$ that is
parallel to the external field. The occurrence of level bifurcations is
explained by invoking semiclassical quantization of the zero field Fermi
surface of rhombohedral graphite. We find parameter regions with a single
isoenergetic contour of Berry phase zero corresponding to a conventional Landau
level spectrum and regions with two isoenergetic contours, each of Berry phase
$\pi$, corresponding to a Dirac-like spectrum of levels. We write down an
analogous one-dimensional tight-binding model and relate the persistence of the
zero-energy bands in large magnetic fields to a soliton texture supporting
zero-energy states in the Su-Schreiffer-Heeger model. We show that different
states contributing to the zero-energy flat bands in rhombohedral graphene
multilayers in a large field, as determined by the wave vector $q$, are
localized on different bulk layers of the system, not just the surfaces.
