  We estimate the evolution of the contribution of galaxies to the cosmic
background flux at $912 \AA$ by means of a semi-analytic model of galaxy
formation and evolution. Such a modelling has been quite successful in
reproducing the optical properties of galaxies. We assume hereafter the
high-redshift damped Lyman-$\alpha$ (DLA) systems to be the progenitors of
present day galaxies, and we design a series of models which are consistent
with the evolution of cosmic comoving emissivities in the available near
infrared (NIR), optical, ultraviolet (UV), and far infrared (FIR) bands along
with the evolution of the neutral hydrogen content and average metallicity of
damped Lyman-$\alpha$ systems (DLA). We use these models to compute the
galactic contribution to the Lyman-limit emissivity and background flux for $0
\simeq z \le 4$. We take into account the absorption of Lyman-limit photons by
HI and dust in the interstellar medium (ISM) of the galaxies. We find that the
background Lyman-limit flux due to galaxies might dominate (or be comparable
to) the contribution from quasars at almost all redshifts if the absorption by
HI in the ISM is neglected. The ISM HI absorption results in a severe
diminishing of this flux--by almost three orders of magnitude at high redshifts
to between one and two orders at $z \simeq 0$. Though the resulting galaxy flux
is completely negligible at high redshifts, it is comparable to the quasar flux
at $z \simeq 0$.
