Genomic response to adaptation is limited by linkage among simultaneously arising favorable mutations. While the dynamics of competing beneficial mutations in asexual populations has been explored in considerable detail, the effects of linkage on adaptation in recombining genomes is less well understood. Motivated by recent evidence for extensive positive selection in genomes of sexually reproducing eukaryotes, we develop a model of the genomic response to adaptation in the presence of recombination. We extend our model of time-dependent selection [Mustonen and Lässig PNAS 104, 2277] to include the effects of linkage. The resulting minimal model of adaptation under linkage demonstrates the existence of an emergent class of quasi neutral mutations: a class of mutations for which the dynamics of substitutions becomes independent of their individual selection coefficients as a result of linkage to ongoing selective sweeps. A self consistent approximation of the substitution dynamics in linked systems leads to applications for standard population genetic observables.