It has been shown by several authors that a certain class of composite
operators with many fields and gradients endangers the stability of n
on-trivial fixed paints in 2 + epsilon expansions for various models.
This problem is up to now unresolved. We investigate it in the N-vecto
r model in an 1/N expansion. By establishing an asymptotic naive addit
ion law for anomalous dimensions we demonstrate that the first orders
in the 2 + epsilon expansion can lead to erroneous interpretations for
high-gradient operators. While this makes us cautious to over-interpr
et such expansions (either 2 + epsilon or 1/N), the stability problem
in the N-vector model persists also in first order in 1/N below three
dimensions. (C) 1997 Elsevier Science B.V.