Allopatric populations of Geospiza difficilis, the Sharp-beaked Ground Finch, differ morphologically in association with different habitats to an extent unrivalled by any other species of Darwin's finch. The question arises as to whether they have diverged so much that they would not interbreed if they became sympatric; in other words, have they become separate species while remaining allopatric? In other species of Darwin's finches, it is known that a sexual imprinting-like process based on early learning of song constrains breeding to conspecifics in sympatry. Therefore we used song playback experiments on Isla Genovesa to test the potential of G. difficilis to respond to songs from two other populations of the species on other, ecologically similar, islands. We found strong responses by males to songs of their own population, and heterogeneous but overall weaker responses to the structurally similar songs of G. difficilis from Isla Darwin. Tested birds did not respond to G. difficilis songs from Isla Wolf, songs of G. fuliginosa from Isla Pinta and control Cassin's finch songs. Female responses were infrequent and weak, apparently inhibited by the presence of responding males in most instances. Thus, assuming that females exercise similar discriminations to those of males, the Genovesa population of G. difficilis appears to be well advanced along the path of speciation: reproductively isolated from the Wolf population by a premating barrier to gene exchange that is culturally inherited, but not reproductively isolated from the Darwin population. We discuss the implications of imprinting for the process of speciation, the reasons for divergence of songs in allopatry, and the outcome of a hypothetical secondary contact in terms of coexistence, competition and interbreeding. © 2002 The Linnean Society of London, Biological Journal of the Linnean Society, 76, 545–556.