  We apply the solution for the strong CP-problem in the 4-dimensional
superstring theory recently proposed by Ib${\rm\acute{a}\tilde{n}}$ez and
L${\rm\ddot{u}}$st to Calabi-Yau type models and study its phenomenological
aspects. In Calabi-Yau type models there seem to be phenomenologically
difficult problems in the axion decoupling from the neutral gauge currents and
the compatibility between the proton stability and the cosmological bound on
the axion. DFSZ type invisible axion mechanism which works without heavy extra
colored fields may be more promising than KSVZ axion in the viewpoint of proton
stability.
