  Axions are produced during a period of dilaton-driven inflation by
amplification of quantum fluctuations. We show that for some range of string
cosmology parameters and some range of axion masses, primordial axions may
constitute a large fraction of the present energy density in the universe in
the form of cold dark matter. Due to the periodic nature of the axion potential
energy density fluctuations are strongly suppressed. The spectrum of primordial
axions is not thermal, allowing a small fraction of the axions to remain
relativistic until quite late.
