Introgression from a resident species into an invading one is predicted to occur through the demographic process of "allele surfing," and to particularly affect genomic regions transmitted by the lower migrating sex, such as mtDNA. This could explain that northern Iberian populations of Lepus granatensis harbor high frequencies of mtDNA from L. timidus, an arctic hare it replaced there after deglaciation. We report that variation of introgressed timidus-like mtDNA reflects several predicted effects of this process: increasing frequency and diversity in the direction of expansion, strong perpendicular phylogeographic structure and signs of postglacial demographic growth. However, demographic inferences for the granatensis and timidus-like mtDNA lineages suggest the latter may have outcompeted the former in northern Iberia. Autosomal introgression occurs at low frequencies and species-wide rather than only in the north. If this difference with mtDNA resulted from sex-biased migration, an intermediate pattern should prevail for the X-chromosome, but we report species-wide and high-frequency introgression of an X-fragment. Either selection favored this ubiquitous X-introgression, or more complex postglacial expansion patterns prevailed, with different consequences depending on the genomic and geographic region. This illustrates the difficulty of distinguishing demographic and selective effects and the need for genome and species-wide based demographic models.