Trans-species polymorphism, meaning the presence of alleles in different species that are more similar to each other than they are to alleles in the same species, has been found at loci associated with vegetative incompatibility in filamentous fungi. If individuals differ at one or more of these loci (termed het for heterokaryon), they cannot form stable heterokaryons after vegetative fusion. At the het-c locus in Neurospora crassa and related species there is clear evidence of trans-species polymorphism: three alleles have persisted for approximately 30 million years. We analyze a population genetic model of multilocus vegetative incompatibility and find the conditions under which trans-species polymorphism will occur. In the model, several unlinked loci determine the vegetative compatibility group (VCG) of an individual. Individuals of different VCGs fail to form productive heterokaryons, while those of the same VCG form viable heterokaryons. However, viable heterokaryon formation between individuals of the same VCG results in a loss in fitness, presumably via transfer of infectious agents by hyphal fusion or exploitation by aggressive genotypes. The result is a form of balancing selection on all loci affecting an individual's VCG. We analyze this model by making use of a Markov chain/strong selection, weak mutation (SSWM) approximation. We find that trans-species polymorphism of the type that has been found at the het-c locus is expected to occur only when the appearance of new incompatibility alleles is strongly constrained, because the rate of mutation to such alleles is very low, because the number of possible incompatibility alleles at each locus is restricted, or because the number of incompatibility loci is limited.