We use the millennium simulation for studying the evolution of groups of galaxies over time. We find fossil and non-fossil groups as well as old and young groups at redshift z = 0 and follow them back in time to investigate the evolution of their parameters, such as mass assembly, luminosity gap and halo mass concentration. We find that fossils assemble a larger fraction of their mass at z = 0 than controls. The magnitude gaps between fossil and non-fossil groups are not the same because of major and minor mergers, in old and young groups as well. We also find that WMAP1 and WMAP7 cosmologies lead to the same evolutionary history for fossil and control groups.