The ${\mathrm{E}}_{8}$ \ensuremath{\bigotimes} E${\ensuremath{'}}_{8}$ superstring models in Calabi-Yau internal space have the cosomological axionic domain-wall problem, ${N}_{\mathrm{DW}}g~2$, if two non-Abelian gauge groups $\mathrm{SU}{(3)}_{c}\ensuremath{\bigotimes}G$ survive. Breaking $G$ down to its Abelian subgroup removes the domain-wall problem. In general, if $\mathrm{SU}{(3)}_{c}$ is the only surviving non-Abelian group of the superstring models, the domain-wall problem is not present, because of the model-independent invisible axion. We also point out an elegant method of solving the axionic domain-wall problem with many would-be axions.