We discuss the problem of constructing models containing an axion and
axion-like particles, motivated by astrophysical observations, with decay
constants at the intermediate scale ranging from 109GeV to 1013GeV. We
present examples in which the axion and axion-like particles arise accidentally
as pseudo Nambu-Goldstone bosons of automatic global chiral symmetries, in
models having exact discrete symmetries.Comment: 4 pages. To appear in the Proceedings of the 10th Patras Workshop on
Axions, WIMPs and WISPs, CERN, 29 June - 04 July 201