  We investigate the evolution of the galaxy merger rate predicted by two
semi-analytical galaxy formation models implemented on the Millennium
Simulation of dark matter structure growth. The fraction of merging galaxy
pairs at each time-step of the simulation is derived from the galaxy catalogues
obtained by the models and the results are compared with various observational
estimates of merger fractions taken from the literature. We find a good match
between the pair fractions derived from the simulation and the observed
counting of galaxy pairs obtained by different sources in the redshift range 0
< z < 1.2. The predicted evolution of the number of galaxy mergers per Gyr
grows with redshift as an exponential rate proportional to (1+z)^m, with m
ranging from 0.6 to 0.8 for 0 < z < 2, depending on the luminosity and mass
ratios of the merging galaxies. Our results are in agreement with recent
observational results that argue for a flat evolution in the fraction of galaxy
mergers since z ~ 1.2. The weak evolution predicted for the galaxy merger rate
in an hierarchical model universe shows that the mass assembly evolution of
galaxies through mergers does not follow the rapid evolution of the halo merger
rate obtained in previous studies.
