An intralocus genetic conflict occurs when a locus is selected in opposing directions in different subsets of a population. Populations with two sexes have the potential to host a pair of distinct intralocus conflicts: sexual antagonism and parental antagonism. In this article, we examine the population genetic consequences of these conflicts for X-linked genes. Both conflicts are capable of maintaining genetic variation in a population, but to different degrees. For weak sexual antagonism, the X chromosome has a higher opportunity for polymorphism than the autosomes. For parental antagonism, there is a very limited opportunity for polymorphism on the X chromosome relative to autosomes or to sexual antagonism. X-linkage introduces an asymmetry in the inheritance and expression of sexually and parentally antagonistic genes that leads to a biased fixation of alleles with certain effects. We find little support for the commonly held intuition that the X chromosome should be biased toward fixing female-beneficial alleles. Contrary to this intuition, we find that the X chromosome is biased toward fixation of male-beneficial alleles for much of the range of dominance. Additionally, we find that the X chromosome is more favorable to the fixation of alleles that are beneficial when maternally derived.