Off-axis electron orbits are investigated for a longitudinal-wiggler f
ree-electron laser. Orbits are found that are very similar to orbits o
ccurring for standard helical wigglers which produce transverse fields
and these orbits can be classified as group-I, group-II, and reverse-
group-II orbits. These orbits are shown to be stable in both first and
second order from Liapounov's first stability theorem. The stability
is verified with numerical simulations.