A protected and warningly coloured butterfly can become a muellerian mimic of another species in two steps: (i) a major mutation converts the pattern of the less protected species to an approximate resemblance of the better protected (one-way convergence); (ii) after the spread of this mutant, the species, which now resemble each other sufficiently to be mistaken one for the other by predators, undergo mutual convergence, using whatever major or minor genetic variation is available to them. Although sometimes one or other step might occur alone, in general early theorists were mistaken in attributing muellerian mimicry to only one of these processes. By hybridizing races of Heliconius melpomene and races of H. erato (a pair of parallel mimetic species from the neotropics, held in mutual muellerian mimicry across wide inter-racial variations in colour pattern) we have shown that, as expected from the two-step theory, the races differ at a number (two to nine) of genetic loci, usually unlinked or loosely linked, including at least one mutant of major effect in each case. We describe the genetic constitution of eight races of H. melpomene (for 11 loci affecting colour pattern) and of eight races of H. erato (for up to 15 loci), and have started to identify the linkage groups. Map distances for those loci that are linked range from around 0.3 to zero in males, with no recombination in females. Muellerian mimicry is expected to produce total uniformity of pattern: universal exceptions to this are the existence of distinct mimicry rings flying within the same habitat, geographical variation within nearly all the more widespread species (divergence in the face of normalizing selection), and, in a few species, polymorphism or sexual dimorphism. Sympatric mimicry rings will, according to the two-step model of evolution, persist indefinitely if their patterns are so distinct that under no circumstances do predators mistake one for the other. Gradual mutual convergence is then impossible, although members of a weakly protected mimicry ring that can produce a mutation giving sufficient initial resemblance to a better protected ring can still be captured by it. Batesian mimics promote this by lowering the protection of the ring that they belong to, but their models can escape only in this way as normalizing selection prevents their gradual evolution away from the batesian mimic. If the rings are too distinct in pattern even this capture of species becomes impossible as no single mutant is able to bridge the gap between the two patterns, and the necessary two mutations will be extremely unlikely to occur together. The five principal sympatric mimicry rings of the mature neotropical rain forests are very distinct in their appearance. The capture of a species by another ring can produce geographical variation both in the species captured and in the capturing ring, whose pattern is somewhat altered by mutual convergence with the captured species in the second step of the evolution of the muellerian resemblance. We suggest that the striking differences between the races within H. melpomene, H. erato and other Heliconius species resulted from these effects of inter-ring capture. Distributional evidence suggests that this chiefly occurred in refuges formed by the contraction of the neotropical rain forests during the cool dry periods in the Quaternary; these, by differential extinction of elements of the flora and fauna of different refuges, could have produced long-term changes in the relative abundances of the mimicry rings, and hence (as the protection given to a ring is proportional to its abundance) somewhat different capture events in each refuge. Several existing species confirm that this mode of evolution occurs, by retaining a distinctive pattern in the absence of any other remotely similar species, but becoming mimetic in areas where they encounter a pattern somewhat like their own. The isolated populations of Heliconius hermathena show this particularly clearly; the effect can be discerned also in H. melpomene and H. erato. Although polymorphism in muellerian mimics is largely unexplained, in two species of Heliconius it may result from the existence of two or more similar but slightly differing 'sub-rings' among their comimics in the family Ithomiidae, which show both spatial and temporal heterogeneity in their local distribution, which apparently is able to maintain a polymorphic equilibrium in the more uniformly distributed Heliconius. We have tentatively reconstructed the ancestral patterns of H. melpomene and erato by two independent methods: first, as dominant genes are much more likely to be incorporated than recessive ones during changes of pattern, the phenotype produced by the recessive alleles at all the known loci will be close to the ancestral pattern; secondly, species that are becoming mimics evolve more than those that are not, so that non-mimetic relatives of melpomene and erato will have a pattern close to ancestral. Both methods suggest, for both species, that the ancestor was a black butterfly with yellow (or possibly white) bars, and it may be that melpomene and erato have been comimics for a very long time. Previous climatic cycles in the Quaternary have apparently caused full speciation within two mutually mimetic evolving lineages, producing pairs of parallel mimetic species within the genus, of which melpomene and erato constitute one pair.