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Abstract Sexual antagonism occurs when males and females differ in their phenotypic fitness optima but are constrained in their evolution to these optima because of their shared genome. The sex chromosomes, which have distinct evolutionary “interests” relative to the autosomes, are theorized to play an important role in sexually antagonistic conflict. However, the evolutionary responses of sex chromosomes and autosomes have usually been considered independently, that is, via contrasting the response of a gene located on either an X chromosome or an autosome. Here, we study the coevolutionary response of the X chromosome and autosomes to sexually antagonistic selection acting on a polygenic phenotype. We model a phenotype initially under stabilizing selection around a single optimum, followed by a sudden divergence of the male and female optima. We find that, in the absence of dosage compensation, the X chromosome promotes evolution toward the female optimum, inducing coevolutionary male-biased responses on the autosomes. Dosage compensation obscures the female-biased interests of the X, causing it to contribute equally to male and female phenotypic change. We further demonstrate that fluctuations in an adaptive landscape can generate prolonged intragenomic conflict and accentuate the differential responses of the X and autosomes to this conflict.