Genes on non-recombining heterogametic sex chromosomes may degrade over time through the irreversible accumulation of deleterious mutations. In papaya, the non-recombining male-specific region of the Y (MSY) consists of two evolutionary strata corresponding to chromosomal inversions occurring approximately 7.0 and 1.9 MYA. The step-wise recombination suppression between the papaya X and Y allows for a temporal examination of the degeneration progress of the young Y chromosome. Comparative evolutionary analyses of 55 X/Y gene pairs showed that Y-linked genes have more unfavorable substitutions than X-linked genes. However, this asymmetric evolutionary pattern is confined to the oldest stratum, and is only observed when recently evolved pseudogenes are included in the analysis, indicating a slow degeneration tempo of the papaya Y chromosome. Population genetic analyses of coding sequence variation of six Y-linked focal loci in the oldest evolutionary stratum detected an excess of nonsynonymous polymorphism and reduced codon bias relative to autosomal loci. However, this pattern was also observed for corresponding X-linked loci. Both the MSY and its corresponding X-specific region are pericentromeric where recombination has been shown to be greatly reduced. Like the MSY region, overall selective efficacy on the X-specific region may be reduced due to the interference of selective forces between highly linked loci, or the Hill-Robertson effect, that is accentuated in regions of low or suppressed recombination. Thus, a pattern of gene decay on the X-specific region may be explained by relaxed purifying selection and widespread genetic hitchhiking due to its pericentromeric location.