  We present calculations of the stability of planar fronts in two mean field
models of diffusion limited growth. The steady state solution for the front can
exist for a continuous family of velocities, we show that the selected velocity
is given by marginal stability theory. We find that naive mean field theory has
no instability to transverse perturbations, while a threshold mean field theory
has such a Mullins-Sekerka instability. These results place on firm theoretical
ground the observed lack of the dendritic morphology in naive mean field theory
and its presence in threshold models. The existence of a Mullins-Sekerka
instability is related to the behavior of the mean field theories in the
zero-undercooling limit.
