Sex chromosomes have evolved independently in several different groups of organisms, but they share common features, including genetic degeneration of the Y chromosome. Suppression of recombination between ancestral proto-X and proto-Y chromosomes is thought to have led to their gradual divergence, and to degeneration of the Y chromosome, but the evolutionary forces responsible are unknown. In non-recombining Y chromosomes, deleterious mutations may be carried to fixation by linked advantageous mutations ("selective sweeps"). Occurrence of deleterious mutations may drive "Muller's ratchet" (stochastic loss of chromosomes with the fewest mutations). Selective elimination of deleterious mutations, causing "background selection" may accelerate stochastic fixation of mildly detrimental mutations. All these processes lower effective population sizes, and therefore reduce variability of genes in evolving Y chromosomes. We have studied DNA diversity and divergence in a recently described X- and Y-linked gene pair (SLX-1 and SLY-1) of the plant Silene latifolia to obtain evidence about the early stages of Y degeneration. Here we show that DNA polymorphism in SLY-1 is 20-fold lower than in SLX-1, but the pattern of polymorphism does not suggest a selective sweep.