  We adapt the L-Galaxies semi-analytic model to follow the star-formation
histories (SFH) of galaxies -- by which we mean a record of the formation time
and metallicities of the stars that are present in each galaxy at a given time.
We use these to construct stellar spectra in post-processing, which offers
large efficiency savings and allows user-defined spectral bands and dust models
to be applied to data stored in the Millennium data repository.
  We contrast model SFHs from the Millennium Simulation with observed ones from
the VESPA algorithm as applied to the SDSS-7 catalogue. The overall agreement
is good, with both simulated and SDSS galaxies showing a steeper SFH with
increased stellar mass. The SFHs of blue and red galaxies, however, show poor
agreement between data and simulations, which may indicate that the termination
of star formation is too abrupt in the models.
  The mean star-formation rate (SFR) of model galaxies is well-defined and is
accurately modelled by a double power law at all redshifts: SFR proportional to
$1/(x^{-1.39}+x^{1.33})$, where $x=(t_a-t)/3.0\,$Gyr, $t$ is the age of the
stars and $t_a$ is the loopback time to the onset of galaxy formation; above a
redshift of unity, this is well approximated by a gamma function: SFR
proportional to $x^{1.5}e^{-x}$, where $x=(t_a-t)/2.0\,$Gyr. Individual
galaxies, however, show a wide dispersion about this mean. When split by mass,
the SFR peaks earlier for high-mass galaxies than for lower-mass ones, and we
interpret this downsizing as a mass-dependence in the evolution of the quenched
fraction: the SFHs of star-forming galaxies show only a weak mass dependence.
