  We have examined a set of pure luminosity evolution (PLE) models in order to
explore up to what extent the rapidly increasing observational constraints from
faint galaxy samples can be understood in this simple framework. We find that a
PLE model, in which galaxies evolve mildly in time even in the rest frame UV,
can reproduce most of the observed properties of faint galaxies assuming an
open ($\Omega\sim0$) universe. In particular, such a model is able to fit
reasonably well the number counts in the $U,~b_j,~r_f,~I$, and $K$ bands, as
well as the colour and redshift distributions derived from most of the existing
samples. The most significant discrepancy between the predictions of this model
and the data is the $z$ distribution of faint $K$-selected galaxies.
Significantly worse fits are obtained with PLE models for the theoretically
attractive value of $\Omega = 1$, although a simple number luminosity evolution
model with a significant amount of merger events fits the data also in this
cosmology.
