Suppose that selection acts at one or more loci to maintain genetic differences between hybridising populations. Then, the flow of alleles at a neutral marker locus which is linked to these selected loci will be impeded. We define and calculate measures of the barrier to gene flow between two distinct demes, and across a continuous habitat. In both cases, we find that in order for gene flow to be significantly reduced over much of the genome, hybrids must be substantially less fit, and the number of genes involved in building the barrier must be so large that the majority of other genes become closely linked to some locus which is under selection. This conclusion is not greatly affected by the pattern of epistasis, or the position of the marker locus along the chromosome.