  We reconsider a cosmological evolution of domain walls produced by
spontaneous breaking of an approxime discrete symmetry. We show, that domain
walls may never collapse even if the standard bound on the vacuum energy
asymmetry is satisfied. Instead of disappearing, these defects may form stable
``bound states'' - double wall systems. Possible stability of such a wall is a
dynamical question and consequently restricts the allowed range of parameters.
In particular, in the two Higgs doublet standard model with an anomalous Z(2)
symmetry, the above restriction suggests the mass of the pseudoscalar Higgs
(would be axion) being close to the mass of the scalar one.
