  We discuss the conditions under which pre-big bang models can fit the
observed large-scale anisotropy with a primordial spectrum of massive
(Kalb--Ramond) axion fluctuations.
  The primordial spectrum must be sufficiently flat at low frequency and
sufficiently steeper at high frequency. For a steep and/or long enough
high-frequency branch of the spectrum the bounds imposed by COBE's
normalization allow axion masses of the typical order for a
Peccei--Quinn--Weinberg--Wilczek axion. We provide a particular example in
which an appropriate axion spectrum is obtained from a class of backgrounds
satisfying the low-energy string cosmology equations.
