A large number of genes is shared by all living organisms, whereas many others are unique to some specific lineages, indicating their different times of origin. The availability of a growing number of eukaryotic genomes allows us to estimate which mammalian genes are novel genes and, approximately, when they arose. In this article, we classify human genes into four different age groups and estimate evolutionary rates in human and mouse orthologs. We show that older genes tend to evolve more slowly than newer ones; that is, proteins that arose earlier in evolution currently have a larger proportion of sites subjected to negative selection. Interestingly, this property is maintained when a fraction of the fastest-evolving genes is excluded or when only genes belonging to a given functional class are considered. One way to explain this relationship is by assuming that genes maintain their functional constraints along all their evolutionary history, but the nature of more recent evolutionary innovations is such that the functional constraints operating on them are increasingly weaker. Alternatively, our results would also be consistent with a scenario in which the functional constraints acting on a gene would not need to be constant through evolution. Instead, starting from weak functional constraints near the time of origin of a gene-as supported by mechanisms proposed for the origin of orphan genes-there would be a gradual increase in selective pressures with time, resulting in fewer accepted mutations in older versus more novel genes.