By hybridization and backcrossing, alleles can surmount species boundaries and get incorporated into the genome of a related species. This introgression of genes is of particular evolutionary relevance if it involves the transfer of adaptations between populations. However, any beneficial allele will typically be associated with other alien alleles, which are often deleterious for various reasons and hence hamper the introgression process. In order to describe the introgression of an adaptive allele, we set up a stochastic model with an explicit genetic makeup of linked and unlinked deleterious alleles. Based on the theory of reducible multitype branching processes, we derive a recursive expression for the establishment probability of the beneficial
allele after a single hybridization event. We furthermore study the probability that slightly deleterious alleles hitchhike to fixation.