We have explored the formation of longitudinal and transverse halos in 3-D axisymmetric beam bunches by starting with a self-consistent 6-D phase space distribution. Stationary distributions allow us to study the halo development mechanism without being obscured by beam redistribution and its effect on halo formation. The beam is then mismatched longitudinally and/or transversely, and we explore the rate, intensity and spatial extent of the halos which form, as a function of the beam charge and the mismatches. We find that the longitudinal halo forms first because the longitudinal tune depression is more severe than the transverse one for elongated bunches and conclude that it plays a major role in halo formation. ©1998 American Institute of Physics.