We predict the observable properties of the galaxy population in sever
al popular hierarchical models of galaxy formation. We employ a detail
ed semi-analytic procedure which incorporates the formation and mergin
g of dark matter haloes, the shock heating and radiative cooling of ga
s, self-regulated star formation, the merging of galaxies within dark
matter haloes, and the spectral evolution of the stellar populations.
We contrast the standard CDM cosmogony with variants of the CDM models
having either a low value of H-0, or a low value of Omega with or wit
hout a cosmological constant. In addition, we compare galaxy formation
in these CDM universes with a 'cold plus hot' dark matter model (CHDM
). The cosmological parameters in these models are constrained by obse
rvations of large-scale structure, light-element abundances, and globu
lar cluster ages, while the astrophysical parameters we determine by a
ttempting to produce the best fit to the present-day observed B-band l
uminosity function. Having fixed the parameters in this manner we gaug
e the success or failure of each model by comparison with other proper
ties of the observed galaxy population: the K-band luminosity function
, the infrared Tully-Fisher relation, B - K colours, number counts and
redshift distributions. We find that, although the models have some s
uccess in remedying the shortcomings of the standard CDM cosmogony, no
ne of these new models produces broad agreement with the whole range o
f observations. Although the low-Omega and Omega + h = 1 CDM models re
duce the discrepancy between the predicted and observed Tully-Fisher r
elations (the main weakness of galaxy formation in standard CDM), thes
e models predict an inverted colour-magnitude relation and do not prod
uce an exponential cut-off at the bright end of the galaxy luminosity
function. All of our models predict recent star formation in the major
ity of galaxies and exhibit galaxy colours bluer than observed, but th
is problem is far more severe in the CHDM model, which produces colour
s about two magnitudes too blue in B - K. The excessively blue colours
in the CHDM model are a direct consequence of the late epoch of struc
ture formation and are independent of our modelling of star formation
and feedback. We discuss several potential refinements to the galaxy f
ormation recipe: the inclusion of metallicity effects, non-local feedb
ack, inhibited star formation in cooling flows and an initial mass fun
ction that varies in time and space.