Author Summary Using recently available marsupial and monotreme genomes, we investigated nascent sex chromosome evolution in mammals. We show that, in eutherian mammals, X and Y genes acquired distinct evolutionary rates and functional constraints immediately after recombination suppression; X-linked genes maintained lower, ancestral (autosomal), rates, whereas the evolutionary rates of Y-linked genes increased. Most X and, unexpectedly, Y genes evolved under stronger purifying selection than similarly aged autosomal paralogs. However, we also observed that the divergence of gametologs and paralogs shared similar features. In addition, many Y-linked copies evolved unique functions and expression patterns compared to their counterparts on the X chromosome. Therefore, our results suggest that to be retained on the Y chromosome, genes need to acquire separately valuable expression and/or functions to be safeguarded by purifying selection.