Axion versus domain walls bounded by cosmic strings

It is shown that two possible schemes of string bounded domain wall formation are closely related. Walls can be avoided if a certain type of couplings between scalars, responsible for string and wall formation, are excluded from the potential. This enlarges the continuous global symmetry of the model which, being broken, instead of domain walls gives rise to global strings and goldstone bosons. A realistic example of spontaneously broken family symmetry is considered. It is shown that the existence of the axion in the model with local chiral flavor symmetry SU(3) sub H, can solve the domain wall problem.