  We analyze the stability of non-ground nonlinear states of a Bose-Einstein
condensate in the mean field limit in effectively 1D (``cigar-shape'') traps
for various types of confining potentials. We find that nonlinear states
become, in general, more stable when switching from a harmonic potential to an
anharmonic one. We discuss the relation between this fact and the specifics of
the harmonic potential which has an equidistant spectrum.
