Regularity of the deformation of the Fermi surface under short-range intera
ctions is established to all orders in perturbation theory. The proofs are
based on a new classification of all graphs that are not doubly overlapping
. They turn out to be generalized RPA graphs. This fact provides a simple e
xtension to all orders of the regularity theorem of the Fermi surface movem
ent proven in [2]. Models in which S is not symmetric under the reflection
p --> -p are included. (C) 1999 John Wiley & Sons, Inc.