Therian X and Y sex chromosomes arose from a pair of autosomes. Y chromosomes consist of a pseudoautosomal region that crosses over with the X chromosome and a male-specific Y-chromosomal region that does not. The X chromosome can be structured into "evolutionary strata". Divergence of X-chromosomal genes from their gametologs is similar within a stratum, but differs among strata, likely caused by a different onset of suppression of crossing over between gametologs. After stratum formation, exchange of information between gametologs has long been believed absent; however, recent studies have shown limited exchange, likely through gene conversion. Herein we investigate exchange of genetic information between gametologs in old strata that formed before the split of Laurasiatheria (cattle) from Euarchontoglires (primates and rodents) with a new phylogenetic approach. A prerequisite for our test is an overall preradiative topology, that is, all X-chromosomal gametologs are more similar among themselves than to Y-chromosomal sequences. Screening multiple sequence alignments of the coding sequences of genes from cattle, mice, and humans identified four genes, DDX3X/Y,RBMX/Y,USP9X/Y, and UTX/Y, exhibiting a preradiation topology. Applying our test, we detected exchange of genetic information between all four X and Y gametologs after stratum formation.